Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
408 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 59 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. #23771284 | C2 | semidirect |
| 5. #23761431 | C2 | semidirect |
| 6. #23761428 | C2 | semidirect |
| 7. C79×#1319 | C2 | semidirect |
| 100. C2×Q8×C79 | SD16 | semidirect |
| 187. #1319 | D79 | semidirect |
| 188. C79 | #12128 | semidirect |
| 256. C2×Q8 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771284 | 2 |
| #23764446 | 2 |
| #23762439 | 2 |
| #23762371 | 2 |
| #23761431 | 2 |
| #23761428 | 2 |
| C79×#1319 | 2 |
| #12128 | 79 |