Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26021226 | C2 | semidirect |
| 5. #26018134 | C2 | semidirect |
| 6. #26018133 | C2 | semidirect |
| 7. C89×#1993 | C2 | semidirect |
| 12. #19151990 | C4 | semidirect |
| 57. #15667923 | C2×C4 | semidirect |
| 67. C4⋊Q8×C89 | C2×C4 | semidirect |
| 224. #1993 | D89 | semidirect |
| 228. C89 | #9003 | semidirect |
| 267. C4⋊Q8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151990 | 2 |
| #26023423 | 2 |
| #26021226 | 2 |
| C2×#19151337 | 2 |
| #26018134 | 2 |
| #26018133 | 2 |
| C89×#1993 | 2 |
| #9003 | 89 |