Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26018196 | C2 | semidirect |
| 3. #26018186 | C2 | semidirect |
| 49. C2×Q8×C89 | M16 | semidirect |
| 79. C42×C89 | M16 | semidirect |
| 146. C89 | #11531 | semidirect |
| 189. C2×Q8 | #13083558 | semidirect |
| 221. C42 | #13083558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018590 | 2 |
| #26018196 | 2 |
| #26018186 | 2 |
| C4×#124×C89 | 2 |
| #11531 | 89 |