Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#19098385 | C2 | semidirect |
| 2. C2×#19098383 | C2 | semidirect |
| 5. #23764129 | C2 | semidirect |
| 6. #23761499 | C2 | semidirect |
| 156. C79 | #13467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098385 | 2 |
| C2×#19098383 | 2 |
| C2×#19098373 | 2 |
| #23764289 | 2 |
| #23764129 | 2 |
| #23761499 | 2 |
| C2×#360×C79 | 2 |
| #13467 | 79 |