Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
572 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 117 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×#106×D89 | C2 | semidirect |
| 3. C2×#19151408 | C2 | semidirect |
| 4. #26021862 | C2 | semidirect |
| 5. #26018359 | C2 | semidirect |
| 6. #26018358 | C2 | semidirect |
| 7. C2×#360×C89 | C2 | semidirect |
| 12. #19151836 | C4 | semidirect |
| 13. #19151831 | C4 | semidirect |
| 49. #15667946 | C2×C4 | semidirect |
| 52. #15667944 | D4 | semidirect |
| 61. C2×Q16×C89 | C2×C4 | semidirect |
| 63. C2×D8×C89 | C2×C4 | semidirect |
| 70. #106×C89 | D4 | semidirect |
| 175. C2×D89 | #360 | semidirect |
| 195. C2×#360 | D89 | semidirect |
| 199. C89 | #13001 | semidirect |
| 226. C2×Q16 | C4×D89 | semidirect |
| 228. C2×D8 | C4×D89 | semidirect |
| 260. #106 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029829 | 2 |
| C2×#106×D89 | 2 |
| C2×#19151408 | 2 |
| #26021862 | 2 |
| #26018359 | 2 |
| #26018358 | 2 |
| C2×#360×C89 | 2 |
| #13001 | 89 |