Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
950 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23771794 | C2 | semidirect |
| 3. #23764229 | C2 | semidirect |
| 4. #23762068 | C2 | semidirect |
| 5. #23762067 | C2 | semidirect |
| 6. #23761232 | C2 | semidirect |
| 7. C79×#3205 | C2 | semidirect |
| 48. C4⋊(C79⋊C8) | D4 | semidirect |
| 58. C4⋊Q8×C79 | D4 | semidirect |
| 63. #127×C79 | D4 | semidirect |
| 70. C4⋊C8×C79 | D4 | semidirect |
| 96. C4×Dic79 | D8 | semidirect |
| 211. #3205 | D79 | semidirect |
| 217. C79 | #10280 | semidirect |
| 250. C4⋊Q8 | C22⋊D79 | semidirect |
| 263. #127 | C22⋊D79 | semidirect |
| 276. C4⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774315 | 2 |
| #23771794 | 2 |
| #23764229 | 2 |
| #23762068 | 2 |
| #23762067 | 2 |
| #23761232 | 2 |
| C79×#3205 | 2 |
| #10280 | 79 |