Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
678 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 678 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 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C32 |
| prime radical | C32×#466 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C22×C32×C4 ◁ C22×C32×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C32×Q16 | C2 | semidirect |
| 2. C2×C32×SD32 | C2 | semidirect |
| 4. C32×#358 | C2 | semidirect |
| 5. C32×C22⋊C16 | C2 | semidirect |
| 6. C3×#2185 | C3 | direct (N × H) |
| 18. C22×C3×Q16 | C2×C3 | semidirect |
| 19. C2×C3×SD32 | C2×C3 | semidirect |
| 21. C3×#358 | C2×C3 | semidirect |
| 22. C3×C22⋊C16 | C2×C3 | semidirect |
| 33. C32×Q16 | D4 | semidirect |
| 41. #2185 | C32 | direct (N × H) |
| 70. C22×Q16 | C2×C32 | semidirect |
| 71. C2×SD32 | C2×C32 | semidirect |
| 73. #358 | C2×C32 | semidirect |
| 74. C22⋊C16 | C2×C32 | semidirect |
| 85. C3×Q16 | C3×D4 | semidirect |
| 98. C22×C32 | SD32 | semidirect |
| 148. Q16 | C32×D4 | semidirect |
| 161. C22×C3 | C3×SD32 | semidirect |
| 168. C32 | #2185 | direct (N × H) |
| 196. C22 | C32×SD32 | semidirect |
| 203. C3 | C3×#2185 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q16 | 2 |
| C2×C32×SD32 | 2 |
| C32×#466 | 2 |
| C32×#358 | 2 |
| C32×C22⋊C16 | 2 |
| C3×#2185 | 3 |