Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
626 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #26018097 | C2 | semidirect |
| 4. #26018096 | C2 | semidirect |
| 5. C89×#1281 | C2 | semidirect |
| 65. C2×#10623494 | M16 | semidirect |
| 79. C2×C8×C89 | M16 | semidirect |
| 137. #1281 | D89 | semidirect |
| 138. C89 | #7919 | semidirect |
| 205. C2×C8 | #13083557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028880 | 2 |
| C2×#97×D89 | 2 |
| #26018097 | 2 |
| #26018096 | 2 |
| C89×#1281 | 2 |
| #7919 | 89 |