Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
662 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26030718 | C2 | semidirect |
| 2. #26030343 | C2 | semidirect |
| 3. #26026104 | C2 | semidirect |
| 4. #26018875 | C2 | semidirect |
| 5. #26018800 | C2 | semidirect |
| 6. #26018117 | C2 | semidirect |
| 7. C89×#1490 | C2 | semidirect |
| 44. #15668012 | D4 | semidirect |
| 45. #15668009 | D4 | semidirect |
| 64. #15667923 | D4 | semidirect |
| 83. C4×C8×C89 | D4 | semidirect |
| 233. #1490 | D89 | semidirect |
| 235. C89 | #10018 | semidirect |
| 307. C4×C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030718 | 2 |
| #26030343 | 2 |
| #26026104 | 2 |
| #26018875 | 2 |
| #26018800 | 2 |
| #26018117 | 2 |
| C89×#1490 | 2 |
| #10018 | 89 |