Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
398 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23765316 | C2 | semidirect |
| 2. #23764723 | C2 | semidirect |
| 3. #23761409 | C2 | semidirect |
| 4. #23761340 | C2 | semidirect |
| 99. C2×C4×C79 | SD32 | semidirect |
| 142. C79 | #12161 | semidirect |
| 246. C2×C4 | #14579105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765316 | 2 |
| #23764723 | 2 |
| #23761409 | 2 |
| #23761340 | 2 |
| C79×#3245 | 2 |
| #12161 | 79 |