Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
384 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 384 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. #23775056 | C2 | semidirect |
| 2. #23765664 | C2 | semidirect |
| 3. #23762876 | C2 | semidirect |
| 4. #23761444 | C2 | semidirect |
| 5. #23761370 | C2 | semidirect |
| 6. #23761357 | C2 | semidirect |
| 7. C79×#2207 | C2 | semidirect |
| 102. Q16×C79 | D8 | semidirect |
| 175. #2207 | D79 | semidirect |
| 180. C79 | #12325 | semidirect |
| 258. Q16 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775056 | 2 |
| #23765664 | 2 |
| #23762876 | 2 |
| #23761444 | 2 |
| #23761370 | 2 |
| #23761357 | 2 |
| C79×#2207 | 2 |
| #12325 | 79 |