Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26028840 | C2 | semidirect |
| 3. #26021988 | C2 | semidirect |
| 4. C2×#19151379 | C2 | semidirect |
| 5. #26018354 | C2 | semidirect |
| 6. #26018353 | C2 | semidirect |
| 7. C89×#2145 | C2 | semidirect |
| 12. #19151853 | C4 | semidirect |
| 13. #19151848 | C4 | semidirect |
| 54. #15667944 | C2×C4 | semidirect |
| 55. #15667944 | D4 | semidirect |
| 64. C2×Q16×C89 | C2×C4 | semidirect |
| 66. C2×D8×C89 | C2×C4 | semidirect |
| 73. #106×C89 | D4 | semidirect |
| 196. #2145 | D89 | semidirect |
| 200. C89 | #13008 | semidirect |
| 226. C2×Q16 | C4×D89 | semidirect |
| 228. C2×D8 | C4×D89 | semidirect |
| 264. #106 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029857 | 2 |
| #26028840 | 2 |
| #26021988 | 2 |
| C2×#19151379 | 2 |
| #26018354 | 2 |
| #26018353 | 2 |
| C89×#2145 | 2 |
| #13008 | 89 |