Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 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. #20295741 | C2 | semidirect |
| 2. #20295376 | C2 | semidirect |
| 3. #20295364 | C2 | semidirect |
| 4. #20295316 | C2 | semidirect |
| 5. #20295257 | C2 | semidirect |
| 6. #20295228 | C2 | semidirect |
| 7. #20295171 | C2 | semidirect |
| 8. C4×#13182014 | C2 | semidirect |
| 9. D4×#11724784 | C2 | semidirect |
| 10. #20295022 | C2 | semidirect |
| 11. #547×C109 | C2 | semidirect |
| 131. C109 | #3303 | semidirect |
| 133. #547 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295741 | 2 |
| #20295376 | 2 |
| #20295364 | 2 |
| #20295316 | 2 |
| #20295257 | 2 |
| #20295228 | 2 |
| #20295171 | 2 |
| C4×#13182014 | 2 |
| D4×#11724784 | 2 |
| #20295022 | 2 |
| #547×C109 | 2 |
| #3303 | 109 |