Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1222 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1222 conjugacy classes of subgroups — too many to draw. Only its 203 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. #23773396 | C2 | semidirect |
| 2. #23768305 | C2 | semidirect |
| 3. #23762403 | C2 | semidirect |
| 4. #23762335 | C2 | semidirect |
| 5. #23761960 | C2 | semidirect |
| 6. #23761724 | C2 | semidirect |
| 7. C79×#3497 | C2 | semidirect |
| 110. C2×Q8×C79 | D8 | semidirect |
| 213. #3497 | D79 | semidirect |
| 220. C79 | #18218 | semidirect |
| 307. C2×Q8 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773396 | 2 |
| #23768305 | 2 |
| #23762403 | 2 |
| #23762335 | 2 |
| #23761960 | 2 |
| #23761724 | 2 |
| C79×#3497 | 2 |
| #18218 | 79 |