Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
690 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 180 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×C32 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C32 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C32×C42 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#562 | C2 | semidirect |
| 2. C32×#496 | C2 | semidirect |
| 3. C32×#490 | C2 | semidirect |
| 4. C32×#330 | C2 | semidirect |
| 5. C32×#329 | C2 | semidirect |
| 6. C3×#1656 | C3 | direct (N × H) |
| 18. C3×#562 | C2×C3 | semidirect |
| 19. C3×#496 | C2×C3 | semidirect |
| 20. C3×#490 | C2×C3 | semidirect |
| 21. C3×#330 | C2×C3 | semidirect |
| 22. C3×#329 | C2×C3 | semidirect |
| 40. #1656 | C32 | direct (N × H) |
| 67. #562 | C2×C32 | semidirect |
| 68. #496 | C2×C32 | semidirect |
| 69. #490 | C2×C32 | semidirect |
| 70. #330 | C2×C32 | semidirect |
| 71. #329 | C2×C32 | semidirect |
| 156. C32 | #1656 | direct (N × H) |
| 186. C3 | C3×#1656 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#562 | 2 |
| C32×#496 | 2 |
| C32×#490 | 2 |
| C32×#330 | 2 |
| C32×#329 | 2 |
| C3×#1656 | 3 |