Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
243 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 243 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 6. C2×C9×M16 | C4 | semidirect |
| 7. C22×C8×C9 | C4 | semidirect |
| 12. #63394 | C4 | semidirect |
| 108. C2×M16 | Dic9 | semidirect |
| 109. C22×C8 | Dic9 | semidirect |
| 175. C9 | #1395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#408 | 2 |
| #10588920 | 2 |
| #10588915 | 2 |
| #67692 | 3 |