Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
345 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 106 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×C4×C8×C9 | C2 | semidirect |
| 4. #10588783 | C2 | semidirect |
| 6. #10588227 | C2 | semidirect |
| 7. #10588201 | C2 | semidirect |
| 17. #63380 | C4 | semidirect |
| 19. #63376 | C4 | semidirect |
| 98. C2×C4×C8 | D9 | semidirect |
| 223. C9 | #1937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C8×C9 | 2 |
| #10588794 | 2 |
| #10588791 | 2 |
| #10588783 | 2 |
| C2×#63364 | 2 |
| #10588227 | 2 |
| #10588201 | 2 |
| #69793 | 3 |