Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
670 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26029280 | C2 | semidirect |
| 3. C4×#15667928 | C2 | semidirect |
| 4. #26018696 | C2 | semidirect |
| 5. #26018694 | C2 | semidirect |
| 6. #26018145 | C2 | semidirect |
| 7. C89×#1300 | C2 | semidirect |
| 62. C4⋊#10623494 | D4 | semidirect |
| 73. C4⋊C8×C89 | D4 | semidirect |
| 253. #1300 | D89 | semidirect |
| 254. C89 | #9031 | semidirect |
| 313. C4⋊C8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029280 | 2 |
| #26023533 | 2 |
| C4×#15667928 | 2 |
| #26018696 | 2 |
| #26018694 | 2 |
| #26018145 | 2 |
| C89×#1300 | 2 |
| #9031 | 89 |