Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20295405 | C2 | semidirect |
| 4. #20294778 | C2 | semidirect |
| 5. #20294772 | C2 | semidirect |
| 6. #20294771 | C2 | semidirect |
| 46. D4×C109 | Q16 | semidirect |
| 79. C109 | #1669 | semidirect |
| 127. D4 | #13182019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295405 | 2 |
| #20295306 | 2 |
| D4×#11724784 | 2 |
| #20294778 | 2 |
| #20294772 | 2 |
| #20294771 | 2 |
| #474×C109 | 2 |
| #1669 | 109 |