Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
328 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 9. #16812753 | C4 | semidirect |
| 10. C4×#11724786 | C4 | semidirect |
| 11. C8×#89137 | C4 | semidirect |
| 15. #16812610 | C4 | semidirect |
| 16. #16812609 | C4 | semidirect |
| 17. #97×C109 | C4 | semidirect |
| 61. C109 | #1726 | semidirect |
| 75. #97 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812753 | 2 |
| C4×D109⋊C8 | 2 |
| C2×C8×#89137 | 2 |
| #20295962 | 2 |
| #97×D109 | 2 |
| #1726 | 109 |