Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
632 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 101 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. #23773404 | C2 | semidirect |
| 3. #23761964 | C2 | semidirect |
| 4. #23761824 | C2 | semidirect |
| 5. #23761791 | C2 | semidirect |
| 6. #23761260 | C2 | semidirect |
| 7. C79×#3077 | C2 | semidirect |
| 56. C4×C79⋊C8 | D4 | semidirect |
| 63. C4⋊Q8×C79 | D4 | semidirect |
| 64. C4⋊Q8×C79 | D4 | semidirect |
| 81. C4⋊C8×C79 | D4 | semidirect |
| 118. C2×D4×C79 | SD16 | semidirect |
| 239. #3077 | D79 | semidirect |
| 245. C79 | #10000 | semidirect |
| 278. C4⋊Q8 | C22⋊D79 | semidirect |
| 279. C4⋊Q8 | C22⋊D79 | semidirect |
| 310. C4⋊C8 | C22⋊D79 | semidirect |
| 337. C2×D4 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773404 | 2 |
| #23768297 | 2 |
| #23761964 | 2 |
| #23761824 | 2 |
| #23761791 | 2 |
| #23761260 | 2 |
| C79×#3077 | 2 |
| #10000 | 79 |