Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
740 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23774338 | C2 | semidirect |
| 3. #23762069 | C2 | semidirect |
| 4. #23761899 | C2 | semidirect |
| 5. #23761791 | C2 | semidirect |
| 6. #23761301 | C2 | semidirect |
| 7. C79×#3077 | C2 | semidirect |
| 47. C4⋊(C79⋊C8) | D4 | semidirect |
| 57. C4⋊Q8×C79 | D4 | semidirect |
| 58. C4⋊Q8×C79 | D4 | semidirect |
| 75. C4⋊C8×C79 | D4 | semidirect |
| 110. C2×D4×C79 | SD16 | semidirect |
| 223. #3077 | D79 | semidirect |
| 229. C79 | #10246 | semidirect |
| 261. C4⋊Q8 | C22⋊D79 | semidirect |
| 262. C4⋊Q8 | C22⋊D79 | semidirect |
| 291. C4⋊C8 | C22⋊D79 | semidirect |
| 324. C2×D4 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774338 | 2 |
| #23768346 | 2 |
| #23762069 | 2 |
| #23761899 | 2 |
| #23761791 | 2 |
| #23761301 | 2 |
| C79×#3077 | 2 |
| #10246 | 79 |