Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23764176 | C2 | semidirect |
| 3. #23762174 | C2 | semidirect |
| 4. #23762150 | C2 | semidirect |
| 6. #23761275 | C2 | semidirect |
| 165. C79 | #10603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764241 | 2 |
| #23764176 | 2 |
| #23762174 | 2 |
| #23762150 | 2 |
| #23762068 | 2 |
| #23761275 | 2 |
| C2×#331×C79 | 2 |
| #10603 | 79 |