Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
794 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23772860 | C2 | semidirect |
| 2. #23768347 | C2 | semidirect |
| 3. #23762068 | C2 | semidirect |
| 4. #23761895 | C2 | semidirect |
| 5. #23761790 | C2 | semidirect |
| 6. #23761302 | C2 | semidirect |
| 7. C79×#3205 | C2 | semidirect |
| 53. C4⋊(C79⋊C8) | D4 | semidirect |
| 64. C4⋊Q8×C79 | D4 | semidirect |
| 69. #127×C79 | D4 | semidirect |
| 76. C4⋊C8×C79 | D4 | semidirect |
| 86. C2×D316 | D8 | semidirect |
| 241. #3205 | D79 | semidirect |
| 248. C79 | #10238 | semidirect |
| 285. C4⋊Q8 | C22⋊D79 | semidirect |
| 292. #127 | C22⋊D79 | semidirect |
| 312. C4⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772860 | 2 |
| #23768347 | 2 |
| #23762068 | 2 |
| #23761895 | 2 |
| #23761790 | 2 |
| #23761302 | 2 |
| C79×#3205 | 2 |
| #10238 | 79 |