Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. #20295376 | C2 | semidirect |
| 3. #20295364 | C2 | semidirect |
| 4. #20295306 | C2 | semidirect |
| 5. #20295265 | C2 | semidirect |
| 6. #20295233 | C2 | semidirect |
| 7. #20295188 | C2 | semidirect |
| 8. C4×#13182017 | C2 | semidirect |
| 9. D4×#11724784 | C2 | semidirect |
| 10. #20295022 | C2 | semidirect |
| 126. C109 | #3302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295746 | 2 |
| #20295376 | 2 |
| #20295364 | 2 |
| #20295306 | 2 |
| #20295265 | 2 |
| #20295233 | 2 |
| #20295188 | 2 |
| C4×#13182017 | 2 |
| D4×#11724784 | 2 |
| #20295022 | 2 |
| #547×C109 | 2 |
| #3302 | 109 |