Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
574 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #26021585 | C2 | semidirect |
| 3. #26021389 | C2 | semidirect |
| 4. #26021337 | C2 | semidirect |
| 5. #26018072 | C2 | semidirect |
| 6. #26018072 | C2 | semidirect |
| 7. C89×#1271 | C2 | semidirect |
| 86. C2×D356 | SD16 | semidirect |
| 130. C4⋊C4×C89 | SD16 | semidirect |
| 234. #1271 | D89 | semidirect |
| 237. C89 | #7778 | semidirect |
| 349. C4⋊C4 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026614 | 2 |
| #26021585 | 2 |
| #26021389 | 2 |
| #26021337 | 2 |
| #26018072 | 2 |
| C89×#1271 | 2 |
| #7778 | 89 |