Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
498 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23772252 | C2 | semidirect |
| 2. #23765136 | C2 | semidirect |
| 3. #23765116 | C2 | semidirect |
| 4. #23764299 | C2 | semidirect |
| 5. #23761502 | C2 | semidirect |
| 6. #23761485 | C2 | semidirect |
| 24. C2×SD32×C79 | C4 | semidirect |
| 25. C2×D16×C79 | C4 | semidirect |
| 52. C2×Q16×C79 | C2×C4 | semidirect |
| 58. C2×D8×C79 | C2×C4 | semidirect |
| 66. C2×C16×C79 | C2×C4 | semidirect |
| 181. C79 | #13033 | semidirect |
| 187. C2×SD32 | Dic79 | semidirect |
| 188. C2×D16 | Dic79 | semidirect |
| 207. C2×Q16 | C2×Dic79 | semidirect |
| 213. C2×D8 | C2×Dic79 | semidirect |
| 231. C2×C16 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772252 | 2 |
| #23765136 | 2 |
| #23765116 | 2 |
| #23764299 | 2 |
| #23761502 | 2 |
| #23761485 | 2 |
| C2×#509×C79 | 2 |
| #13033 | 79 |