Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20295749 | C2 | semidirect |
| 3. #20295373 | C2 | semidirect |
| 4. #20295353 | C2 | semidirect |
| 5. #20295311 | C2 | semidirect |
| 6. #20295258 | C2 | semidirect |
| 7. #20295226 | C2 | semidirect |
| 8. #20295187 | C2 | semidirect |
| 9. C8×D436 | C2 | semidirect |
| 10. #20295021 | C2 | semidirect |
| 11. C4×Q16×C109 | C2 | semidirect |
| 128. C109 | #3304 | semidirect |
| 137. C4×Q16 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295749 | 2 |
| #20295698 | 2 |
| #20295373 | 2 |
| #20295353 | 2 |
| #20295311 | 2 |
| #20295258 | 2 |
| #20295226 | 2 |
| #20295187 | 2 |
| C8×D436 | 2 |
| #20295021 | 2 |
| C4×Q16×C109 | 2 |
| #3304 | 109 |