Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
318 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10588707 | C2 | semidirect |
| 3. #10588515 | C2 | semidirect |
| 5. C9×Q8⋊C8 | C2 | semidirect |
| 7. #10588133 | C2 | semidirect |
| 104. Q8⋊C8 | D9 | semidirect |
| 224. C9 | #1640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589687 | 2 |
| #10588707 | 2 |
| #10588515 | 2 |
| #10588376 | 2 |
| C9×Q8⋊C8 | 2 |
| #10588163 | 2 |
| #10588133 | 2 |
| #68262 | 3 |