Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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. #20295996 | C2 | semidirect |
| 2. #20295871 | C2 | semidirect |
| 3. #20295869 | C2 | semidirect |
| 49. C23×C109 | M16 | semidirect |
| 54. C2×C4×C109 | M16 | semidirect |
| 98. C109 | #1465 | semidirect |
| 147. C23 | #13182038 | semidirect |
| 165. C2×C4 | #13182038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295996 | 2 |
| #20295871 | 2 |
| #20295869 | 2 |
| C2×D4×Dic109 | 2 |
| #1465 | 109 |