Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
399 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 399 conjugacy classes of subgroups — too many to draw. Only its 78 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. C22×D72 | C2 | semidirect |
| 2. C9×#466 | C2 | semidirect |
| 3. C2×#63385 | C2 | semidirect |
| 4. #10588226 | C2 | semidirect |
| 5. #10588168 | C2 | semidirect |
| 8. C2×C9×D8 | C22 | semidirect |
| 14. C9×#107 | C22 | semidirect |
| 17. C2×C9⋊C16 | C22 | semidirect |
| 39. D72 | D4 | semidirect |
| 74. #466 | D9 | semidirect |
| 100. C22×C9 | D16 | semidirect |
| 114. C2×D8 | C2×D9 | semidirect |
| 119. #107 | C2×D9 | semidirect |
| 179. C9 | #2184 | semidirect |
| 214. C22 | #63385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D72 | 2 |
| C9×#466 | 2 |
| C2×#63385 | 2 |
| #10588226 | 2 |
| #10588168 | 2 |
| #71075 | 3 |