Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23776534 | C2 | semidirect |
| 2. #23773846 | C2 | semidirect |
| 3. #23765127 | C2 | semidirect |
| 4. #23761480 | C2 | semidirect |
| 5. C79×#1975 | C2 | semidirect |
| 47. C2×C79⋊C16 | D4 | semidirect |
| 51. C2×Q16×C79 | D4 | semidirect |
| 53. C2×D8×C79 | D4 | semidirect |
| 167. #1975 | D79 | semidirect |
| 169. C79 | #13340 | semidirect |
| 199. C2×Q16 | D316 | semidirect |
| 205. C2×D8 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776534 | 2 |
| #23773846 | 2 |
| #23765127 | 2 |
| #23761480 | 2 |
| C79×#1975 | 2 |
| #13340 | 79 |