Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#16812729 | C2 | semidirect |
| 2. C2×C4×Dic218 | C2 | semidirect |
| 3. #20295245 | C2 | semidirect |
| 4. #20295233 | C2 | semidirect |
| 5. #20295223 | C2 | semidirect |
| 6. #20295050 | C2 | semidirect |
| 7. #20295027 | C2 | semidirect |
| 36. C2×Dic218 | D4 | semidirect |
| 110. C4×C109 | #137 | semidirect |
| 121. C109 | #3037 | semidirect |
| 233. C4 | #16812729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812729 | 2 |
| C2×C4×Dic218 | 2 |
| #20295245 | 2 |
| #20295233 | 2 |
| #20295223 | 2 |
| #20295050 | 2 |
| #20295027 | 2 |
| #532×C109 | 2 |
| #3037 | 109 |