Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23776534 | C2 | semidirect |
| 2. #23772981 | C2 | semidirect |
| 3. #23765136 | C2 | semidirect |
| 4. #23765135 | C2 | semidirect |
| 5. #23765011 | C2 | semidirect |
| 6. #23761501 | C2 | semidirect |
| 7. C79×#3050 | C2 | semidirect |
| 38. C2×Dic316 | D4 | semidirect |
| 40. C2×D632 | D4 | semidirect |
| 56. C2×C79⋊C16 | D4 | semidirect |
| 58. #14579093 | D4 | semidirect |
| 67. C2×Q16×C79 | D4 | semidirect |
| 69. C2×D8×C79 | D4 | semidirect |
| 85. #106×C79 | D4 | semidirect |
| 235. #3050 | D79 | semidirect |
| 240. C79 | #13309 | semidirect |
| 278. C2×Q16 | C22⋊D79 | semidirect |
| 282. C2×D8 | C22⋊D79 | semidirect |
| 316. #106 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776534 | 2 |
| #23772981 | 2 |
| #23765136 | 2 |
| #23765135 | 2 |
| #23765011 | 2 |
| #23761501 | 2 |
| C79×#3050 | 2 |
| #13309 | 79 |