Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. #23765201 | C2 | semidirect |
| 3. #23762154 | C2 | semidirect |
| 4. #23761370 | C2 | semidirect |
| 5. #23761368 | C2 | semidirect |
| 6. #23761366 | C2 | semidirect |
| 7. C79×#1334 | C2 | semidirect |
| 74. D632 | M16 | semidirect |
| 95. Q16×C79 | M16 | semidirect |
| 161. #1334 | D79 | semidirect |
| 164. C79 | #11666 | semidirect |
| 231. Q16 | #11929607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579184 | 2 |
| #23765201 | 2 |
| #23762154 | 2 |
| #23761370 | 2 |
| #23761368 | 2 |
| #23761366 | 2 |
| C79×#1334 | 2 |
| #11666 | 79 |