Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
612 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 612 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×C32 | #121 |
| 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×#493 | C2 | semidirect |
| 2. C32×#459 | C2 | semidirect |
| 3. C32×C8×D4 | C2 | semidirect |
| 4. C32×#335 | C2 | semidirect |
| 5. C32×#331 | C2 | semidirect |
| 6. C3×#1667 | C3 | direct (N × H) |
| 18. C3×#493 | C2×C3 | semidirect |
| 19. C3×#459 | C2×C3 | semidirect |
| 20. C3×C8×D4 | C2×C3 | semidirect |
| 21. C3×#335 | C2×C3 | semidirect |
| 22. C3×#331 | C2×C3 | semidirect |
| 39. #1667 | C32 | direct (N × H) |
| 59. C32×D4 | D8 | semidirect |
| 69. C32×C8 | D8 | semidirect |
| 70. #493 | C2×C32 | semidirect |
| 71. #459 | C2×C32 | semidirect |
| 72. C8×D4 | C2×C32 | semidirect |
| 73. #335 | C2×C32 | semidirect |
| 74. #331 | C2×C32 | semidirect |
| 123. C3×D4 | C3×D8 | semidirect |
| 133. C3×C8 | C3×D8 | semidirect |
| 168. C32 | #1667 | direct (N × H) |
| 177. D4 | C32×D8 | semidirect |
| 187. C8 | C32×D8 | semidirect |
| 206. C3 | C3×#1667 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#493 | 2 |
| C32×#459 | 2 |
| C32×C8×D4 | 2 |
| C32×#335 | 2 |
| C32×#331 | 2 |
| C3×#1667 | 3 |