Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2004 conjugacy classes of subgroups; only the 361 normal subgroups are shown.
This group has 2004 conjugacy classes of subgroups — too many to draw. Only its 361 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×#127 | C2 | semidirect |
| 2. C22×#3754 | C2 | semidirect |
| 3. C22×#3753 | C2 | semidirect |
| 4. C2×#64084 | C2 | semidirect |
| 5. #10592773 | C2 | direct (N × H) |
| 6. C2×#63630 | C2 | semidirect |
| 13. C32×#127 | C22 | semidirect |
| 16. C2×#3754 | C22 | semidirect |
| 18. C2×#3753 | C22 | semidirect |
| 22. #64084 | C22 | semidirect |
| 23. #63630 | C22 | semidirect |
| 24. C2×C3×#127 | D3 | semidirect |
| 52. C2×C3⋊(C3⋊C8) | D4 | semidirect |
| 60. C3×#127 | C2×D3 | semidirect |
| 93. C3⋊(C3⋊C8) | C2×D4 | semidirect |
| 96. C2×#127 | C3⋊D3 | semidirect |
| 147. #127 | C2×C3⋊D3 | semidirect |
| 177. C2×C32 | #496 | semidirect |
| 218. C32 | C2×#496 | semidirect |
| 243. C2×C3 | #5074 | semidirect |
| 260. C3 | C2×#5074 | semidirect |
| 263. C2 | #10592773 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#127 | 2 |
| C22×#3754 | 2 |
| C22×#3753 | 2 |
| C2×#64084 | 2 |
| #10592773 | 2 |
| C2×#63630 | 2 |
| C2×#5074 | 3 |