Finite Group DatabasebetaFinite Group DatabasebetaOrder 28544.
1112 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 360 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×C223 | C22⋊C4 |
| commutator | C22 | C23×C4×C223 |
| Frattini, cosocle | C23 | C24×C223 |
| prime radical | C23×D4×C223 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C223 ◁ C25×C223 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C22⋊C4×C223 | C2 | semidirect |
| 3. C2×#99×C223 | C2 | direct (N × H) |
| 4. C25×C223 | C4 | semidirect |
| 8. C22×D4×C223 | C4 | semidirect |
| 11. C23×C4×C223 | C4 | semidirect |
| 13. C2×C22⋊C4×C223 | C22 | semidirect |
| 14. #99×C223 | C22 | direct (N × H) |
| 21. C24×C223 | C2×C4 | semidirect |
| 29. C2×D4×C223 | C2×C4 | semidirect |
| 35. C22×C4×C223 | C2×C4 | semidirect |
| 37. C22⋊C4×C223 | C23 | semidirect |
| 54. C23×C223 | C22×C4 | semidirect |
| 64. C2×C4×C223 | C22×C4 | semidirect |
| 77. C22×C223 | #99 | direct (N × H) |
| 90. C2×C223 | C2×#99 | direct (N × H) |
| 92. C223 | C22×#99 | direct (N × H) |
| 93. C22×#99 | C223 | direct (N × H) |
| 95. C22×C22⋊C4 | C2×C223 | semidirect |
| 96. C2×#99 | C2×C223 | direct (N × H) |
| 97. C25 | C4×C223 | semidirect |
| 101. C22×D4 | C4×C223 | semidirect |
| 104. C23×C4 | C4×C223 | semidirect |
| 106. C2×C22⋊C4 | C22×C223 | semidirect |
| 107. #99 | C22×C223 | direct (N × H) |
| 114. C24 | C2×C4×C223 | semidirect |
| 122. C2×D4 | C2×C4×C223 | semidirect |
| 128. C22×C4 | C2×C4×C223 | semidirect |
| 130. C22⋊C4 | C23×C223 | semidirect |
| 147. C23 | C22×C4×C223 | semidirect |
| 157. C2×C4 | C22×C4×C223 | semidirect |
| 170. C22 | #99×C223 | direct (N × H) |
| 183. C2 | C2×#99×C223 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D4×C223 | 2 |
| C22×C22⋊C4×C223 | 2 |
| C2×#99×C223 | 2 |
| C22×#99 | 223 |