Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
672 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26021926 | C2 | semidirect |
| 4. #26021905 | C2 | semidirect |
| 6. #26018381 | C2 | semidirect |
| 7. C89×#1391 | C2 | semidirect |
| 9. C2×#15668045 | C4 | semidirect |
| 10. C22×#13083563 | C4 | semidirect |
| 18. #19151604 | C4 | semidirect |
| 20. #19151595 | C4 | semidirect |
| 37. C22×Dic178 | C2×C4 | semidirect |
| 60. #15667971 | C2×C4 | semidirect |
| 74. C2×M16×C89 | C2×C4 | semidirect |
| 75. C22×C8×C89 | C2×C4 | semidirect |
| 258. #1391 | D89 | semidirect |
| 259. C89 | #13100 | semidirect |
| 304. C2×M16 | C4×D89 | semidirect |
| 305. C22×C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029531 | 2 |
| #26028711 | 2 |
| #26021926 | 2 |
| #26021905 | 2 |
| #26020220 | 2 |
| #26018381 | 2 |
| C89×#1391 | 2 |
| #13100 | 89 |