Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
420 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 88 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. C2×C9×#100 | C2 | semidirect |
| 3. C2×#63393 | C2 | semidirect |
| 4. #10588153 | C2 | semidirect |
| 5. #10588152 | C2 | semidirect |
| 8. C22×#611 | C4 | semidirect |
| 12. C2×#3676 | C4 | semidirect |
| 15. #63499 | C4 | semidirect |
| 17. #63497 | C4 | semidirect |
| 31. C23×D9 | C2×C4 | semidirect |
| 47. C22×Dic9 | C2×C4 | semidirect |
| 56. #3676 | C2×C4 | semidirect |
| 57. #3676 | C2×C4 | semidirect |
| 116. C2×#100 | D9 | semidirect |
| 299. C9 | #2121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589906 | 2 |
| C2×C9×#100 | 2 |
| C2×#63393 | 2 |
| #10588153 | 2 |
| #10588152 | 2 |
| #70094 | 3 |