Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 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. #23773116 | C2 | semidirect |
| 2. #23773058 | C2 | semidirect |
| 3. C2×#19098373 | C2 | semidirect |
| 4. #23765128 | C2 | semidirect |
| 5. #23765027 | C2 | semidirect |
| 6. #23761499 | C2 | semidirect |
| 7. C79×#3414 | C2 | semidirect |
| 57. #14579097 | D4 | semidirect |
| 75. C2×Q16×C79 | D4 | semidirect |
| 79. C2×D8×C79 | D4 | semidirect |
| 87. C2×C16×C79 | D4 | semidirect |
| 227. #3414 | D79 | semidirect |
| 234. C79 | #13318 | semidirect |
| 277. C2×Q16 | C22⋊D79 | semidirect |
| 281. C2×D8 | C22⋊D79 | semidirect |
| 306. C2×C16 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773116 | 2 |
| #23773058 | 2 |
| C2×#19098373 | 2 |
| #23765128 | 2 |
| #23765027 | 2 |
| #23761499 | 2 |
| C79×#3414 | 2 |
| #13318 | 79 |