Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16812720 | C2 | semidirect |
| 2. #20295574 | C2 | semidirect |
| 3. C4×#13182030 | C2 | semidirect |
| 4. #20295246 | C2 | semidirect |
| 5. #20295240 | C2 | semidirect |
| 6. #20295236 | C2 | semidirect |
| 7. #20295232 | C2 | semidirect |
| 8. #20295218 | C2 | semidirect |
| 9. C4⋊C8×D109 | C2 | semidirect |
| 10. #20295019 | C2 | semidirect |
| 11. #460×C109 | C2 | semidirect |
| 45. #13182030 | D4 | semidirect |
| 136. C4×C109 | #135 | semidirect |
| 151. C109 | #3035 | semidirect |
| 159. #460 | D109 | semidirect |
| 292. C4 | #16812720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812720 | 2 |
| #20295574 | 2 |
| C4×#13182030 | 2 |
| #20295246 | 2 |
| #20295240 | 2 |
| #20295236 | 2 |
| #20295232 | 2 |
| #20295218 | 2 |
| C4⋊C8×D109 | 2 |
| #20295019 | 2 |
| #460×C109 | 2 |
| #3035 | 109 |