Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26033386 | C2 | semidirect |
| 2. #26029833 | C2 | semidirect |
| 3. #26021988 | C2 | semidirect |
| 4. #26021987 | C2 | semidirect |
| 5. #26021863 | C2 | semidirect |
| 6. #26018353 | C2 | semidirect |
| 7. C89×#3050 | C2 | semidirect |
| 38. C2×Dic356 | D4 | semidirect |
| 40. C2×D712 | D4 | semidirect |
| 56. C2×#13083549 | D4 | semidirect |
| 58. #15667944 | D4 | semidirect |
| 67. C2×Q16×C89 | D4 | semidirect |
| 69. C2×D8×C89 | D4 | semidirect |
| 85. #106×C89 | D4 | semidirect |
| 235. #3050 | D89 | semidirect |
| 240. C89 | #13309 | semidirect |
| 278. C2×Q16 | C22⋊D89 | semidirect |
| 282. C2×D8 | C22⋊D89 | semidirect |
| 316. #106 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033386 | 2 |
| #26029833 | 2 |
| #26021988 | 2 |
| #26021987 | 2 |
| #26021863 | 2 |
| #26018353 | 2 |
| C89×#3050 | 2 |
| #13309 | 89 |