Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
548 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26030291 | C2 | semidirect |
| 3. #26018815 | C2 | semidirect |
| 4. #26018681 | C2 | semidirect |
| 6. #26018110 | C2 | semidirect |
| 107. C2×D4×C89 | Q16 | semidirect |
| 221. C89 | #10002 | semidirect |
| 307. C2×D4 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030291 | 2 |
| #26030049 | 2 |
| #26018815 | 2 |
| #26018681 | 2 |
| #26018643 | 2 |
| #26018110 | 2 |
| C89×#2580 | 2 |
| #10002 | 89 |