Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
170 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 14. C4⋊C4×C349 | C4 | semidirect |
| 39. C4×C349 | C4⋊C4 | semidirect |
| 50. C349 | #389 | semidirect |
| 64. C4⋊C4 | Dic349 | semidirect |
| 93. C4 | C4⋊Dic349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Dic349 | 2 |
| C2×C4×Dic349 | 2 |
| #26013546 | 2 |
| C2×C4⋊C4×C349 | 2 |
| #389 | 349 |