Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 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×#504 | C2 | semidirect |
| 3. #10588821 | C2 | semidirect |
| 4. C2×#63359 | C2 | semidirect |
| 5. #10588195 | C2 | semidirect |
| 6. #10588193 | C2 | semidirect |
| 7. #10588183 | C2 | semidirect |
| 84. #504 | D9 | semidirect |
| 181. C9 | #2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#504 | 2 |
| #10588823 | 2 |
| #10588821 | 2 |
| C2×#63359 | 2 |
| #10588195 | 2 |
| #10588193 | 2 |
| #10588183 | 2 |
| #71455 | 3 |