Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20295571 | C2 | semidirect |
| 2. #20295430 | C2 | semidirect |
| 3. #20295401 | C2 | semidirect |
| 4. #20295371 | C2 | semidirect |
| 5. #20295262 | C2 | semidirect |
| 6. #20295260 | C2 | semidirect |
| 7. D8×Dic109 | C2 | semidirect |
| 8. #20295108 | C2 | semidirect |
| 9. #20295106 | C2 | semidirect |
| 10. C2×C8×Dic109 | C2 | semidirect |
| 11. #466×C109 | C2 | semidirect |
| 89. C2×Dic109 | D8 | semidirect |
| 99. C8×C109 | #41 | semidirect |
| 101. #11724784 | #41 | semidirect |
| 128. C109 | #3169 | semidirect |
| 135. #466 | D109 | semidirect |
| 229. C8 | #13182028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295571 | 2 |
| #20295430 | 2 |
| #20295401 | 2 |
| #20295371 | 2 |
| #20295262 | 2 |
| #20295260 | 2 |
| D8×Dic109 | 2 |
| #20295108 | 2 |
| #20295106 | 2 |
| C2×C8×Dic109 | 2 |
| #466×C109 | 2 |
| #3169 | 109 |