Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26013546 | C2 | semidirect |
| 4. #26013546 | C2 | semidirect |
| 5. C2×C4⋊C4×C349 | C2 | semidirect |
| 50. C349 | #397 | semidirect |
| 52. C2×C4⋊C4 | D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150210 | 2 |
| #26013546 | 2 |
| C2×C4⋊C4×C349 | 2 |
| #397 | 349 |