Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 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. #20295754 | C2 | semidirect |
| 3. #20295377 | C2 | semidirect |
| 4. #20295375 | C2 | semidirect |
| 5. #20295311 | C2 | semidirect |
| 6. #20295310 | C2 | semidirect |
| 9. C8×Dic218 | C2 | semidirect |
| 95. Dic218 | SD16 | semidirect |
| 119. C109 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295754 | 2 |
| D4×Dic218 | 2 |
| #20295377 | 2 |
| #20295375 | 2 |
| #20295311 | 2 |
| #20295310 | 2 |
| #20295231 | 2 |
| #20295229 | 2 |
| C8×Dic218 | 2 |
| #20295117 | 2 |
| C4×SD16×C109 | 2 |
| #3359 | 109 |