Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
480 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C19 |
| prime radical | C22×D4×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C19×C4⋊Q8 | C2 | semidirect |
| 3. C19×#476 | C2 | direct (N × H) |
| 4. C2×C19×#106 | C2 | semidirect |
| 5. C2×C19×C4⋊C8 | C2 | semidirect |
| 12. C19×C4⋊Q8 | C22 | semidirect |
| 20. C19×#106 | C22 | semidirect |
| 21. C19×C4⋊C8 | C22 | semidirect |
| 28. C2×D4×C19 | Q8 | semidirect |
| 55. D4×C19 | C2×Q8 | semidirect |
| 70. C2×#476 | C19 | direct (N × H) |
| 86. C2×C4⋊Q8 | C2×C19 | semidirect |
| 88. #476 | C2×C19 | direct (N × H) |
| 89. C2×#106 | C2×C19 | semidirect |
| 90. C2×C4⋊C8 | C2×C19 | semidirect |
| 93. C2×C19 | #476 | direct (N × H) |
| 102. C4⋊Q8 | C22×C19 | semidirect |
| 110. #106 | C22×C19 | semidirect |
| 111. C4⋊C8 | C22×C19 | semidirect |
| 113. C19 | C2×#476 | direct (N × H) |
| 119. C2×D4 | Q8×C19 | semidirect |
| 146. D4 | C2×Q8×C19 | semidirect |
| 177. C2 | C19×#476 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C19×C4⋊Q8 | 2 |
| C2×C4×D4×C19 | 2 |
| C19×#476 | 2 |
| C2×C19×#106 | 2 |
| C2×C19×C4⋊C8 | 2 |
| C2×C19×#102 | 2 |
| C2×#476 | 19 |