Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20295839 | C2 | semidirect |
| 2. #20295468 | C2 | semidirect |
| 3. #20295467 | C2 | semidirect |
| 4. #20295459 | C2 | semidirect |
| 5. #20295458 | C2 | semidirect |
| 6. Q32×D109 | C2 | semidirect |
| 7. #20295442 | C2 | semidirect |
| 8. C2×Q32×C109 | C2 | semidirect |
| 82. C109 | #3417 | semidirect |
| 89. C2×Q32 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295839 | 2 |
| #20295468 | 2 |
| #20295467 | 2 |
| #20295459 | 2 |
| #20295458 | 2 |
| Q32×D109 | 2 |
| #20295442 | 2 |
| C2×Q32×C109 | 2 |
| #3417 | 109 |