Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23776536 | C2 | semidirect |
| 2. #23776534 | C2 | semidirect |
| 3. #23773843 | C2 | semidirect |
| 4. #23765127 | C2 | semidirect |
| 5. #23764291 | C2 | semidirect |
| 6. #23761479 | C2 | semidirect |
| 7. C79×#2143 | C2 | semidirect |
| 48. C2×Dic316 | D4 | semidirect |
| 55. C2×D632 | D4 | semidirect |
| 75. C2×C79⋊C16 | D4 | semidirect |
| 92. C2×C16×C79 | D4 | semidirect |
| 239. #2143 | D79 | semidirect |
| 242. C79 | #13340 | semidirect |
| 323. C2×C16 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776536 | 2 |
| #23776534 | 2 |
| #23773843 | 2 |
| #23765127 | 2 |
| #23764291 | 2 |
| #23761479 | 2 |
| C79×#2143 | 2 |
| #13340 | 79 |