Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
522 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 204 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 |
| 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. C2×C32×D16 | C2 | semidirect |
| 2. C22×C32×C16 | C2 | semidirect |
| 3. C32×#466 | C2 | semidirect |
| 4. C32×#366 | C2 | semidirect |
| 5. C32×#357 | C2 | semidirect |
| 6. C3×#2215 | C3 | direct (N × H) |
| 16. C2×C3×D16 | C2×C3 | semidirect |
| 17. C22×C3×C16 | C2×C3 | semidirect |
| 18. C3×#466 | C2×C3 | semidirect |
| 19. C3×#366 | C2×C3 | semidirect |
| 20. C3×#357 | C2×C3 | semidirect |
| 33. C32×C16 | D4 | semidirect |
| 34. #2215 | C32 | direct (N × H) |
| 57. C2×D16 | C2×C32 | semidirect |
| 58. C22×C16 | C2×C32 | semidirect |
| 59. #466 | C2×C32 | semidirect |
| 60. #366 | C2×C32 | semidirect |
| 61. #357 | C2×C32 | semidirect |
| 74. C3×C16 | C3×D4 | semidirect |
| 80. C22×C32 | D16 | semidirect |
| 125. C16 | C32×D4 | semidirect |
| 131. C22×C3 | C3×D16 | semidirect |
| 137. C32 | #2215 | direct (N × H) |
| 161. C22 | C32×D16 | semidirect |
| 167. C3 | C3×#2215 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D16 | 2 |
| C22×C32×C16 | 2 |
| C32×#466 | 2 |
| C32×#366 | 2 |
| C32×#357 | 2 |
| C3×#2215 | 3 |