Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
574 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23764728 | C2 | semidirect |
| 2. #23764536 | C2 | semidirect |
| 3. #23764482 | C2 | semidirect |
| 4. #23761223 | C2 | semidirect |
| 5. #23761221 | C2 | semidirect |
| 6. #23761221 | C2 | semidirect |
| 119. C4⋊C4×C79 | SD16 | semidirect |
| 237. C79 | #7752 | semidirect |
| 349. C4⋊C4 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764728 | 2 |
| #23764536 | 2 |
| #23764482 | 2 |
| #23761223 | 2 |
| #23761221 | 2 |
| C79×#2682 | 2 |
| #7752 | 79 |