Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
414 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26021413 | C2 | semidirect |
| 3. #26019262 | C2 | semidirect |
| 5. #26018259 | C2 | semidirect |
| 7. C89×#1319 | C2 | semidirect |
| 101. C2×Q8×C89 | SD16 | semidirect |
| 190. #1319 | D89 | semidirect |
| 191. C89 | #12210 | semidirect |
| 254. C2×Q8 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027221 | 2 |
| #26021413 | 2 |
| #26019262 | 2 |
| #26019194 | 2 |
| #26018259 | 2 |
| #26018256 | 2 |
| C89×#1319 | 2 |
| #12210 | 89 |