Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
394 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 3. #23762442 | C2 | semidirect |
| 4. #23761430 | C2 | semidirect |
| 5. #23761428 | C2 | semidirect |
| 7. C79×#1605 | C2 | semidirect |
| 66. C2×D316 | Q16 | semidirect |
| 183. #1605 | D79 | semidirect |
| 187. C79 | #12223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771103 | 2 |
| #23764553 | 2 |
| #23762442 | 2 |
| #23761430 | 2 |
| #23761428 | 2 |
| #23761331 | 2 |
| C79×#1605 | 2 |
| #12223 | 79 |