Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
198 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 198 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. #20295431 | C2 | semidirect |
| 2. #20295424 | C2 | semidirect |
| 5. #20295377 | C2 | semidirect |
| 7. #322×C109 | C2 | semidirect |
| 54. C8×C109 | SD16 | semidirect |
| 70. C109 | #1714 | semidirect |
| 77. #322 | D109 | semidirect |
| 124. C8 | #13182018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295431 | 2 |
| #20295424 | 2 |
| #20295399 | 2 |
| #20295377 | 2 |
| #20295373 | 2 |
| #322×C109 | 2 |
| #1714 | 109 |