Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
190 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 69 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×C4⋊Dic349 | C2 | semidirect |
| 5. C2×C4×Dic349 | C2 | semidirect |
| 6. #26013546 | C2 | semidirect |
| 7. #95×C349 | C2 | semidirect |
| 15. #19150210 | C4 | semidirect |
| 74. C349 | #388 | semidirect |
| 82. #95 | D349 | 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×#19150210 | 2 |
| C2×C4×Dic349 | 2 |
| #26013546 | 2 |
| #95×C349 | 2 |
| #388 | 349 |