Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20295746 | C2 | semidirect |
| 2. #20295372 | C2 | semidirect |
| 3. #20295347 | C2 | semidirect |
| 4. #20295311 | C2 | semidirect |
| 5. #20295253 | C2 | semidirect |
| 6. #20295223 | C2 | semidirect |
| 7. #20295188 | C2 | semidirect |
| 8. C4×#13182019 | C2 | semidirect |
| 9. D4×#11724784 | C2 | semidirect |
| 10. #20295022 | C2 | semidirect |
| 128. C109 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295746 | 2 |
| #20295372 | 2 |
| #20295347 | 2 |
| #20295311 | 2 |
| #20295253 | 2 |
| #20295223 | 2 |
| #20295188 | 2 |
| C4×#13182019 | 2 |
| D4×#11724784 | 2 |
| #20295022 | 2 |
| #550×C109 | 2 |
| #3304 | 109 |