Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
480 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23764541 | C2 | semidirect |
| 3. #23764499 | C2 | semidirect |
| 4. #23761226 | C2 | semidirect |
| 5. #23761226 | C2 | semidirect |
| 94. C2×D4×C79 | Q16 | semidirect |
| 212. C79 | #7782 | semidirect |
| 284. C2×D4 | #11929614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764541 | 2 |
| #23764536 | 2 |
| #23764499 | 2 |
| #23761226 | 2 |
| #23761221 | 2 |
| C79×#2804 | 2 |
| #7782 | 79 |