Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
356 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 146 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. #20296078 | C2 | semidirect |
| 2. #20296056 | C2 | semidirect |
| 3. #20296056 | C2 | semidirect |
| 4. #20296054 | C2 | semidirect |
| 5. #20296051 | C2 | semidirect |
| 6. #20296049 | C2 | semidirect |
| 7. #20296033 | C2 | semidirect |
| 8. D109⋊(C4⋊C8) | C2 | semidirect |
| 115. C109 | #2992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296078 | 2 |
| #20296056 | 2 |
| #20296054 | 2 |
| #20296051 | 2 |
| #20296049 | 2 |
| #20296033 | 2 |
| D109⋊(C4⋊C8) | 2 |
| #20295561 | 2 |
| #2992 | 109 |