Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
280 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 10. #16812767 | C4 | semidirect |
| 11. C8×#89137 | C4 | semidirect |
| 15. #16812631 | C4 | semidirect |
| 16. #16812630 | C4 | semidirect |
| 17. #106×C109 | C4 | semidirect |
| 57. C8×C109 | C42 | semidirect |
| 58. #11724784 | C42 | semidirect |
| 66. #89137 | #106 | direct (N × H) |
| 79. C109 | C4×#106 | semidirect |
| 94. #106 | #89137 | direct (N × H) |
| 137. C8 | C4×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812767 | 2 |
| C2×C8×#89137 | 2 |
| C4⋊C4×#89137 | 2 |
| #20295899 | 2 |
| #106×D109 | 2 |
| C4×#106 | 109 |