Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
230 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 3. #23762219 | C2 | semidirect |
| 4. #23761465 | C2 | semidirect |
| 6. #23761322 | C2 | semidirect |
| 7. C79×#1334 | C2 | semidirect |
| 26. #14579104 | C8 | semidirect |
| 55. C79⋊C16 | C2×C8 | semidirect |
| 58. Q16×C79 | C2×C8 | semidirect |
| 107. #1334 | D79 | semidirect |
| 110. C79 | #12065 | semidirect |
| 151. Q16 | C8×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765262 | 2 |
| #23762223 | 2 |
| #23762219 | 2 |
| #23761465 | 2 |
| #23761368 | 2 |
| #23761322 | 2 |
| C79×#1334 | 2 |
| #12065 | 79 |