Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
720 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. C4×#15667927 | C2 | semidirect |
| 4. #26018376 | C2 | semidirect |
| 5. C4×#99×C89 | C2 | semidirect |
| 7. C2×C4×D356 | C4 | semidirect |
| 12. #19151499 | C4 | semidirect |
| 15. #19151467 | C4 | semidirect |
| 17. C42×Dic89 | C4 | semidirect |
| 18. #19151390 | C4 | direct (N × H) |
| 49. #15667927 | C2×C4 | semidirect |
| 63. #99×C89 | C2×C4 | semidirect |
| 69. C2×D356 | C42 | semidirect |
| 99. C4×Dic89 | C42 | semidirect |
| 213. C4×C89 | #353 | semidirect |
| 230. C4×#99 | D89 | semidirect |
| 232. C89 | C4×#353 | semidirect |
| 289. #99 | C4×D89 | semidirect |
| 444. C4 | #19151390 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668008 | 2 |
| C2×#19151390 | 2 |
| C4×#15667927 | 2 |
| #26018376 | 2 |
| C4×#99×C89 | 2 |
| C4×#353 | 89 |