Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
342 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 96 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. C9×#428 | C2 | semidirect |
| 3. C2×#63381 | C2 | semidirect |
| 5. #10588677 | C2 | semidirect |
| 7. #10588207 | C2 | semidirect |
| 99. #428 | D9 | semidirect |
| 238. C9 | #2063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#428 | 2 |
| C2×#63383 | 2 |
| C2×#63381 | 2 |
| #10588682 | 2 |
| #10588677 | 2 |
| C2×#63369 | 2 |
| #10588207 | 2 |
| #70676 | 3 |