Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #20295434 | C2 | semidirect |
| 4. #20295433 | C2 | semidirect |
| 5. #20295428 | C2 | semidirect |
| 6. #20295425 | C2 | semidirect |
| 7. #20295425 | C2 | semidirect |
| 11. #499×C109 | C2 | semidirect |
| 43. #13182012 | Q8 | semidirect |
| 44. #13182012 | Q8 | semidirect |
| 100. C109 | #3166 | semidirect |
| 108. #499 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295582 | 2 |
| #125×D109 | 2 |
| #20295434 | 2 |
| #20295433 | 2 |
| #20295428 | 2 |
| #20295425 | 2 |
| #20295067 | 2 |
| #20295065 | 2 |
| C4×#13182012 | 2 |
| #499×C109 | 2 |
| #3166 | 109 |