Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
384 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10588753 | C2 | semidirect |
| 3. #10588703 | C2 | semidirect |
| 4. #10588691 | C2 | semidirect |
| 5. #10588221 | C2 | semidirect |
| 6. #10588212 | C2 | semidirect |
| 7. D4⋊(C9⋊C8) | C2 | semidirect |
| 79. Q8×C9 | SD16 | semidirect |
| 241. C9 | #1631 | semidirect |
| 246. Q8 | #3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#550 | 2 |
| #10588753 | 2 |
| #10588703 | 2 |
| #10588691 | 2 |
| #10588221 | 2 |
| #10588212 | 2 |
| D4⋊(C9⋊C8) | 2 |
| #71919 | 3 |