Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
286 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 286 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 |
|---|---|---|
| 1. C23×Dic349 | C2 | semidirect |
| 2. C2×C22⋊Dic349 | C2 | semidirect |
| 3. C2×C22⋊Dic349 | C2 | semidirect |
| 4. #26013546 | C2 | semidirect |
| 16. C2×D4×C349 | C4 | semidirect |
| 24. C2×Dic349 | D4 | semidirect |
| 32. C23×C349 | C2×C4 | semidirect |
| 39. C2×C4×C349 | C2×C4 | semidirect |
| 49. C22×C349 | C22⋊C4 | semidirect |
| 65. C349 | #386 | semidirect |
| 76. C2×D4 | Dic349 | semidirect |
| 91. C23 | C2×Dic349 | semidirect |
| 105. C2×C4 | C2×Dic349 | semidirect |
| 115. C22 | C22⋊Dic349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic349 | 2 |
| C2×C22⋊Dic349 | 2 |
| #26013546 | 2 |
| C22×D4×C349 | 2 |
| #386 | 349 |