Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
604 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 604 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. C2×#19098998 | C2 | semidirect |
| 2. #23773005 | C2 | semidirect |
| 3. C2×#19098817 | C2 | semidirect |
| 4. #23765117 | C2 | semidirect |
| 5. C2×#19098344 | C2 | semidirect |
| 6. #23761507 | C2 | semidirect |
| 7. C2×#360×C79 | C2 | semidirect |
| 39. C2×D632 | D4 | semidirect |
| 59. #14579101 | D4 | semidirect |
| 61. #14579095 | D4 | semidirect |
| 71. C2×Q16×C79 | D4 | semidirect |
| 73. C2×D8×C79 | D4 | semidirect |
| 80. #106×C79 | D4 | semidirect |
| 224. C2×#360 | D79 | semidirect |
| 228. C79 | #13316 | semidirect |
| 260. C2×Q16 | D316 | semidirect |
| 268. C2×D8 | D316 | semidirect |
| 298. #106 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098998 | 2 |
| #23773005 | 2 |
| C2×#19098817 | 2 |
| #23765117 | 2 |
| C2×#19098344 | 2 |
| #23761507 | 2 |
| C2×#360×C79 | 2 |
| #13316 | 79 |