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. #23776536 | C2 | semidirect |
| 2. #23773121 | C2 | semidirect |
| 3. #23773063 | C2 | semidirect |
| 4. C2×#19098372 | C2 | semidirect |
| 5. #23765127 | C2 | semidirect |
| 6. #23765027 | C2 | semidirect |
| 7. C79×#1383 | C2 | semidirect |
| 50. C2×Dic316 | D4 | semidirect |
| 54. C2×D632 | D4 | semidirect |
| 83. C2×C16×C79 | D4 | semidirect |
| 85. #108×C79 | D4 | semidirect |
| 233. #1383 | D79 | semidirect |
| 234. C79 | #13318 | semidirect |
| 306. C2×C16 | D316 | semidirect |
| 308. #108 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776536 | 2 |
| #23773121 | 2 |
| #23773063 | 2 |
| C2×#19098372 | 2 |
| #23765127 | 2 |
| #23765027 | 2 |
| C79×#1383 | 2 |
| #13318 | 79 |