Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 498 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 | #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×#500 | C2 | semidirect |
| 4. C32×#334 | C2 | semidirect |
| 5. C32×#332 | C2 | semidirect |
| 6. C3×#1693 | C3 | direct (N × H) |
| 18. C3×#500 | C2×C3 | semidirect |
| 21. C3×#334 | C2×C3 | semidirect |
| 22. C3×#332 | C2×C3 | semidirect |
| 37. #1693 | C32 | direct (N × H) |
| 63. C32×C8 | SD16 | semidirect |
| 64. #500 | C2×C32 | semidirect |
| 67. #334 | C2×C32 | semidirect |
| 68. #332 | C2×C32 | semidirect |
| 118. C3×C8 | C3×SD16 | semidirect |
| 147. C32 | #1693 | direct (N × H) |
| 162. C8 | C32×SD16 | semidirect |
| 177. C3 | C3×#1693 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#500 | 2 |
| C32×#461 | 2 |
| C32×#436 | 2 |
| C32×#334 | 2 |
| C32×#332 | 2 |
| C3×#1693 | 3 |