Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
526 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26021293 | C2 | semidirect |
| 2. #26019254 | C2 | semidirect |
| 3. #26019186 | C2 | semidirect |
| 4. #26018258 | C2 | semidirect |
| 5. #26018255 | C2 | semidirect |
| 6. #26018184 | C2 | semidirect |
| 7. C89×#2699 | C2 | semidirect |
| 102. C2×D4×C89 | D8 | semidirect |
| 223. #2699 | D89 | semidirect |
| 230. C89 | #12099 | semidirect |
| 312. C2×D4 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021293 | 2 |
| #26019254 | 2 |
| #26019186 | 2 |
| #26018258 | 2 |
| #26018255 | 2 |
| #26018184 | 2 |
| C89×#2699 | 2 |
| #12099 | 89 |