Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 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. #20295754 | C2 | semidirect |
| 2. #20295380 | C2 | semidirect |
| 4. #20295326 | C2 | semidirect |
| 5. #20295311 | C2 | semidirect |
| 6. #20295245 | C2 | semidirect |
| 8. Q8×#11724784 | C2 | semidirect |
| 9. C4×#13182019 | C2 | semidirect |
| 10. C4×#13182017 | C2 | semidirect |
| 118. C109 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295754 | 2 |
| #20295380 | 2 |
| #20295372 | 2 |
| #20295326 | 2 |
| #20295311 | 2 |
| #20295245 | 2 |
| #20295223 | 2 |
| Q8×#11724784 | 2 |
| C4×#13182019 | 2 |
| C4×#13182017 | 2 |
| #559×C109 | 2 |
| #3365 | 109 |