Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
294 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 294 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 |
|---|---|---|
| 4. #23761452 | C2 | semidirect |
| 5. #23761382 | C2 | semidirect |
| 6. #23761370 | C2 | semidirect |
| 7. C79×#3390 | C2 | semidirect |
| 75. Q16×C79 | SD16 | semidirect |
| 140. #3390 | D79 | semidirect |
| 147. C79 | #12361 | semidirect |
| 208. Q16 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765643 | 2 |
| #23765440 | 2 |
| #23762884 | 2 |
| #23761452 | 2 |
| #23761382 | 2 |
| #23761370 | 2 |
| C79×#3390 | 2 |
| #12361 | 79 |