Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
632 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23773193 | C2 | semidirect |
| 3. #23761964 | C2 | semidirect |
| 4. #23761825 | C2 | semidirect |
| 5. #23761792 | C2 | semidirect |
| 6. #23761259 | C2 | semidirect |
| 7. C79×#3101 | C2 | semidirect |
| 52. C4⋊(C79⋊C8) | D4 | semidirect |
| 63. C4⋊Q8×C79 | D4 | semidirect |
| 64. C4⋊Q8×C79 | D4 | semidirect |
| 83. C4×C8×C79 | D4 | semidirect |
| 90. C2×D316 | SD16 | semidirect |
| 238. #3101 | D79 | semidirect |
| 245. C79 | #10000 | semidirect |
| 278. C4⋊Q8 | C22⋊D79 | semidirect |
| 279. C4⋊Q8 | C22⋊D79 | semidirect |
| 318. C4×C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773193 | 2 |
| #23768301 | 2 |
| #23761964 | 2 |
| #23761825 | 2 |
| #23761792 | 2 |
| #23761259 | 2 |
| C79×#3101 | 2 |
| #10000 | 79 |