Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
794 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 101 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. #23774315 | C2 | semidirect |
| 2. #23772860 | C2 | semidirect |
| 3. #23768342 | C2 | semidirect |
| 4. #23762067 | C2 | semidirect |
| 5. #23761792 | C2 | semidirect |
| 6. #23761303 | C2 | semidirect |
| 7. C79×#1502 | C2 | semidirect |
| 58. C4⋊(C79⋊C8) | D4 | semidirect |
| 59. C4⋊(C79⋊C8) | D4 | semidirect |
| 66. C4⋊Q8×C79 | D4 | semidirect |
| 67. #127×C79 | D4 | semidirect |
| 102. C2×D316 | D8 | semidirect |
| 245. #1502 | D79 | semidirect |
| 248. C79 | #10238 | semidirect |
| 285. C4⋊Q8 | D316 | semidirect |
| 292. #127 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774315 | 2 |
| #23772860 | 2 |
| #23768342 | 2 |
| #23762067 | 2 |
| #23761792 | 2 |
| #23761303 | 2 |
| C79×#1502 | 2 |
| #10238 | 79 |