Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
396 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 2. C2×C9×#106 | C2 | semidirect |
| 3. C2×#63372 | C2 | semidirect |
| 5. #10588207 | C2 | semidirect |
| 13. #63464 | C4 | semidirect |
| 90. C2×#106 | D9 | semidirect |
| 207. C9 | #1815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63464 | 2 |
| C2×C9×#106 | 2 |
| C2×#63372 | 2 |
| #10588649 | 2 |
| #10588207 | 2 |
| #70592 | 3 |