Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1018 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #120 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C24×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C19×H(5,𝔽2) | C2 | semidirect |
| 2. C2×C19×#120 | C2 | semidirect |
| 3. C19×B(4,𝔽2) | C2 | direct (N × H) |
| 4. C2×C19×#99 | C2 | semidirect |
| 5. C25×C19 | C22 | semidirect |
| 7. C19×H(5,𝔽2) | C22 | semidirect |
| 13. C19×#120 | C22 | semidirect |
| 15. C2×C22⋊C4×C19 | C22 | semidirect |
| 16. C19×#99 | C22 | semidirect |
| 21. C24×C19 | D4 | semidirect |
| 23. C24×C19 | C23 | semidirect |
| 34. C2×D4×C19 | D4 | semidirect |
| 38. C22×C4×C19 | D4 | semidirect |
| 41. C22⋊C4×C19 | C23 | semidirect |
| 57. C23×C19 | C2×D4 | semidirect |
| 69. C2×C4×C19 | C2×D4 | semidirect |
| 70. C2×B(4,𝔽2) | C19 | direct (N × H) |
| 89. C2×H(5,𝔽2) | C2×C19 | semidirect |
| 90. C2×#120 | C2×C19 | semidirect |
| 91. B(4,𝔽2) | C2×C19 | direct (N × H) |
| 92. C2×#99 | C2×C19 | semidirect |
| 97. C2×C19 | B(4,𝔽2) | direct (N × H) |
| 99. C25 | C22×C19 | semidirect |
| 101. H(5,𝔽2) | C22×C19 | semidirect |
| 107. #120 | C22×C19 | semidirect |
| 109. C2×C22⋊C4 | C22×C19 | semidirect |
| 110. #99 | C22×C19 | semidirect |
| 111. C19 | C2×B(4,𝔽2) | direct (N × H) |
| 116. C24 | D4×C19 | semidirect |
| 118. C24 | C23×C19 | semidirect |
| 129. C2×D4 | D4×C19 | semidirect |
| 133. C22×C4 | D4×C19 | semidirect |
| 136. C22⋊C4 | C23×C19 | semidirect |
| 152. C23 | C2×D4×C19 | semidirect |
| 164. C2×C4 | C2×D4×C19 | semidirect |
| 187. C2 | C19×B(4,𝔽2) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C19×H(5,𝔽2) | 2 |
| C2×C19×#120 | 2 |
| C19×B(4,𝔽2) | 2 |
| C2×C19×#99 | 2 |
| C2×B(4,𝔽2) | 19 |