Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. C2×#19098610 | C2 | semidirect |
| 3. #23765129 | C2 | semidirect |
| 4. #23765127 | C2 | semidirect |
| 5. C2×#19098344 | C2 | semidirect |
| 6. #23761516 | C2 | semidirect |
| 7. C79×#1389 | C2 | semidirect |
| 57. #14579097 | D4 | semidirect |
| 68. #108×C79 | D4 | semidirect |
| 191. #1389 | D79 | semidirect |
| 192. C79 | #12998 | semidirect |
| 251. #108 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773010 | 2 |
| C2×#19098610 | 2 |
| #23765129 | 2 |
| #23765127 | 2 |
| C2×#19098344 | 2 |
| #23761516 | 2 |
| C79×#1389 | 2 |
| #12998 | 79 |