Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
414 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23764561 | C2 | semidirect |
| 2. #23762407 | C2 | semidirect |
| 4. #23761406 | C2 | semidirect |
| 6. #23761334 | C2 | semidirect |
| 84. C2×Q8×C79 | SD16 | semidirect |
| 191. C79 | #12210 | semidirect |
| 254. C2×Q8 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764561 | 2 |
| #23762407 | 2 |
| #23762339 | 2 |
| #23761406 | 2 |
| #23761403 | 2 |
| #23761334 | 2 |
| C79×#2728 | 2 |
| #12210 | 79 |