Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1040 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1040 conjugacy classes of subgroups — too many to draw. Only its 115 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. C22×#15667927 | C2 | semidirect |
| 2. C2×#19151391 | C2 | semidirect |
| 3. #26020167 | C2 | semidirect |
| 4. #26018377 | C2 | semidirect |
| 15. C2×#127×C89 | C4 | semidirect |
| 17. C2×#121×C89 | C4 | semidirect |
| 22. #390×C89 | C4 | semidirect |
| 24. C4×C22⋊C4×C89 | C4 | semidirect |
| 38. #15667927 | D4 | semidirect |
| 52. C22×D4×C89 | C2×C4 | semidirect |
| 64. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 71. C2×C42×C89 | C2×C4 | semidirect |
| 72. C2×C42×C89 | C2×C4 | semidirect |
| 297. C22×C89 | #353 | semidirect |
| 327. C89 | #13088 | semidirect |
| 329. C2×#127 | Dic89 | semidirect |
| 331. C2×#121 | Dic89 | semidirect |
| 342. #390 | Dic89 | semidirect |
| 345. C4×C22⋊C4 | Dic89 | semidirect |
| 360. C22×D4 | C2×Dic89 | semidirect |
| 373. C2×C4⋊C4 | C2×Dic89 | semidirect |
| 387. C2×C42 | C2×Dic89 | semidirect |
| 388. C2×C42 | C2×Dic89 | semidirect |
| 619. C22 | #19151391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667927 | 2 |
| C2×#19151391 | 2 |
| #26020167 | 2 |
| #26018377 | 2 |
| C89×#2433 | 2 |
| #13088 | 89 |