Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#19150210 | C2 | semidirect |
| 3. C2×C4×Dic349 | C2 | semidirect |
| 4. C2×C4⋊C4×C349 | C2 | semidirect |
| 8. C2×D1396 | C4 | semidirect |
| 23. C2×Dic349 | D4 | semidirect |
| 41. C4×C349 | C22⋊C4 | semidirect |
| 49. C349 | #390 | semidirect |
| 52. C2×C4⋊C4 | D349 | semidirect |
| 92. C4 | #19150210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1396 | 2 |
| C2×#19150210 | 2 |
| C2×C4×Dic349 | 2 |
| C2×C4⋊C4×C349 | 2 |
| #390 | 349 |