Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
| 2. Q8×D436 | C2 | semidirect |
| 3. #20295386 | C2 | semidirect |
| 4. #20295377 | C2 | semidirect |
| 5. #20295322 | C2 | semidirect |
| 6. #20295307 | C2 | semidirect |
| 8. #20295232 | C2 | semidirect |
| 9. #20295128 | C2 | semidirect |
| 11. #446×C109 | C2 | semidirect |
| 123. C109 | #3367 | semidirect |
| 132. #446 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295749 | 2 |
| Q8×D436 | 2 |
| #20295386 | 2 |
| #20295377 | 2 |
| #20295322 | 2 |
| #20295307 | 2 |
| #20295242 | 2 |
| #20295232 | 2 |
| #20295128 | 2 |
| C4×D872 | 2 |
| #446×C109 | 2 |
| #3367 | 109 |