Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 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. #20295741 | C2 | semidirect |
| 2. #20295681 | C2 | semidirect |
| 3. #20295377 | C2 | semidirect |
| 4. #20295368 | C2 | semidirect |
| 5. #20295317 | C2 | semidirect |
| 6. #20295255 | C2 | semidirect |
| 7. #20295232 | C2 | semidirect |
| 8. #20295173 | C2 | semidirect |
| 9. C4×D872 | C2 | semidirect |
| 10. #20295023 | C2 | semidirect |
| 11. C8×D4×C109 | C2 | semidirect |
| 131. C109 | #3303 | semidirect |
| 141. C8×D4 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295741 | 2 |
| #20295681 | 2 |
| #20295377 | 2 |
| #20295368 | 2 |
| #20295317 | 2 |
| #20295255 | 2 |
| #20295232 | 2 |
| #20295173 | 2 |
| C4×D872 | 2 |
| #20295023 | 2 |
| C8×D4×C109 | 2 |
| #3303 | 109 |