Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 2. #20295429 | C2 | semidirect |
| 3. #20295359 | C2 | semidirect |
| 4. #20295350 | C2 | semidirect |
| 5. #20295311 | C2 | semidirect |
| 6. #20295303 | C2 | semidirect |
| 7. #20295274 | C2 | semidirect |
| 8. C4×#13182016 | C2 | semidirect |
| 9. #20295104 | C2 | semidirect |
| 10. #20295069 | C2 | semidirect |
| 11. #556×C109 | C2 | semidirect |
| 99. #11724784 | #41 | semidirect |
| 123. C109 | #3353 | semidirect |
| 124. #556 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295680 | 2 |
| #20295429 | 2 |
| #20295359 | 2 |
| #20295350 | 2 |
| #20295311 | 2 |
| #20295303 | 2 |
| #20295274 | 2 |
| C4×#13182016 | 2 |
| #20295104 | 2 |
| #20295069 | 2 |
| #556×C109 | 2 |
| #3353 | 109 |