Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
310 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 66 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. #20296105 | C2 | semidirect |
| 2. #20296025 | C2 | semidirect |
| 3. #20296016 | C2 | semidirect |
| 4. #20296001 | C2 | semidirect |
| 5. #20295909 | C2 | semidirect |
| 6. #20295901 | C2 | semidirect |
| 25. #16812730 | C4 | semidirect |
| 26. #16812727 | C4 | semidirect |
| 28. #16812724 | C4 | semidirect |
| 32. #137×C109 | C4 | semidirect |
| 146. C109 | #1881 | semidirect |
| 158. #137 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296105 | 2 |
| #20296025 | 2 |
| #20296016 | 2 |
| #20296001 | 2 |
| #20295909 | 2 |
| #20295901 | 2 |
| #20295825 | 2 |
| #1881 | 109 |