Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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×#16812722 | C2 | semidirect |
| 2. C2×#16812707 | C2 | semidirect |
| 3. #20295606 | C2 | semidirect |
| 4. #20295281 | C2 | semidirect |
| 5. #20295280 | C2 | semidirect |
| 6. #20295279 | C2 | semidirect |
| 7. #20295258 | C2 | semidirect |
| 8. #20295257 | C2 | semidirect |
| 9. #106×D109 | C2 | semidirect |
| 10. #20295026 | C2 | semidirect |
| 11. #470×C109 | C2 | semidirect |
| 65. C8×D109 | D4 | semidirect |
| 140. C109 | #3060 | semidirect |
| 145. #470 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812722 | 2 |
| C2×#16812707 | 2 |
| #20295606 | 2 |
| #20295281 | 2 |
| #20295280 | 2 |
| #20295279 | 2 |
| #20295258 | 2 |
| #20295257 | 2 |
| #106×D109 | 2 |
| #20295026 | 2 |
| #470×C109 | 2 |
| #3060 | 109 |