Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
516 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 516 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 |
| prime radical | C2×C32×D4 | D4 |
| 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×#494 | C2 | semidirect |
| 4. C32×#335 | C2 | semidirect |
| 5. C32×#332 | C2 | semidirect |
| 6. C3×#1669 | C3 | direct (N × H) |
| 18. C3×#494 | C2×C3 | semidirect |
| 21. C3×#335 | C2×C3 | semidirect |
| 22. C3×#332 | C2×C3 | semidirect |
| 38. #1669 | C32 | direct (N × H) |
| 54. C32×D4 | Q16 | semidirect |
| 66. #494 | C2×C32 | semidirect |
| 69. #335 | C2×C32 | semidirect |
| 70. #332 | C2×C32 | semidirect |
| 112. C3×D4 | C3×Q16 | semidirect |
| 154. C32 | #1669 | direct (N × H) |
| 159. D4 | C32×Q16 | semidirect |
| 186. C3 | C3×#1669 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#494 | 2 |
| C32×#474 | 2 |
| C32×C8×D4 | 2 |
| C32×#335 | 2 |
| C32×#332 | 2 |
| C3×#1669 | 3 |