Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1480 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1480 conjugacy classes of subgroups — too many to draw. Only its 203 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. C2×#19151911 | C2 | semidirect |
| 3. #26019237 | C2 | direct (N × H) |
| 4. C2×#19151331 | C2 | semidirect |
| 5. C2×#19151322 | C2 | semidirect |
| 6. C2×#397×C89 | C2 | semidirect |
| 16. #19151911 | C22 | semidirect |
| 19. C2×C22⋊#10623494 | C22 | semidirect |
| 20. #19151331 | C22 | semidirect |
| 21. #19151322 | C22 | semidirect |
| 22. C22×C4⋊C4×C89 | C22 | semidirect |
| 26. #397×C89 | C22 | semidirect |
| 28. C2×#95×C89 | C22 | semidirect |
| 57. C22⋊#10623494 | C23 | semidirect |
| 66. C2×C4⋊C4×C89 | C23 | semidirect |
| 75. #95×C89 | C23 | semidirect |
| 231. C2×C89 | #1607 | semidirect |
| 238. C2×#397 | D89 | semidirect |
| 242. C89 | C2×#1607 | semidirect |
| 251. C22×C4⋊C4 | C2×D89 | semidirect |
| 260. #397 | C2×D89 | semidirect |
| 262. C2×#95 | C2×D89 | semidirect |
| 296. C2×C4⋊C4 | C22×D89 | semidirect |
| 311. #95 | C22×D89 | semidirect |
| 467. C2 | #26019237 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152160 | 2 |
| C2×#19151911 | 2 |
| #26019237 | 2 |
| C2×#19151331 | 2 |
| C2×#19151322 | 2 |
| C2×#397×C89 | 2 |
| C2×#1607 | 89 |