Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23776356 | C2 | semidirect |
| 2. #23765642 | C2 | semidirect |
| 4. #23762885 | C2 | semidirect |
| 5. #23761453 | C2 | semidirect |
| 6. #23761383 | C2 | semidirect |
| 7. C79×#1333 | C2 | semidirect |
| 89. D8×C79 | SD16 | semidirect |
| 152. #1333 | D79 | semidirect |
| 153. C79 | #12360 | semidirect |
| 221. D8 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776356 | 2 |
| #23765642 | 2 |
| #23765435 | 2 |
| #23762885 | 2 |
| #23761453 | 2 |
| #23761383 | 2 |
| C79×#1333 | 2 |
| #12360 | 79 |