Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
612 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26028196 | C2 | semidirect |
| 2. #26021340 | C2 | semidirect |
| 4. #26018078 | C2 | semidirect |
| 5. #26018077 | C2 | semidirect |
| 6. #26018072 | C2 | semidirect |
| 7. C89×#2014 | C2 | semidirect |
| 75. C2×D356 | SD16 | semidirect |
| 242. #2014 | D89 | semidirect |
| 247. C89 | #7745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028196 | 2 |
| #26021340 | 2 |
| #26021323 | 2 |
| #26018078 | 2 |
| #26018077 | 2 |
| #26018072 | 2 |
| C89×#2014 | 2 |
| #7745 | 89 |