Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
740 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26030045 | C2 | semidirect |
| 3. #26018920 | C2 | semidirect |
| 4. #26018751 | C2 | semidirect |
| 5. #26018642 | C2 | semidirect |
| 6. #26018154 | C2 | semidirect |
| 7. C89×#3208 | C2 | semidirect |
| 51. C4⋊#10623494 | D4 | semidirect |
| 61. C4⋊Q8×C89 | D4 | semidirect |
| 62. C4⋊Q8×C89 | D4 | semidirect |
| 74. C4⋊C8×C89 | D4 | semidirect |
| 84. C2×D356 | SD16 | semidirect |
| 222. #3208 | D89 | semidirect |
| 229. C89 | #10246 | semidirect |
| 261. C4⋊Q8 | C22⋊D89 | semidirect |
| 262. C4⋊Q8 | C22⋊D89 | semidirect |
| 291. C4⋊C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030045 | 2 |
| #26025199 | 2 |
| #26018920 | 2 |
| #26018751 | 2 |
| #26018642 | 2 |
| #26018154 | 2 |
| C89×#3208 | 2 |
| #10246 | 89 |