Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. C2×#16812768 | C2 | semidirect |
| 3. C2×#16812767 | C2 | semidirect |
| 5. #20295900 | C2 | semidirect |
| 6. #20295900 | C2 | semidirect |
| 23. C22⋊#11724784 | C4 | semidirect |
| 24. #16812611 | C4 | semidirect |
| 25. #16812611 | C4 | semidirect |
| 26. C22⋊C8×C109 | C4 | semidirect |
| 141. C109 | #1854 | semidirect |
| 166. C22⋊C8 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812778 | 2 |
| C2×#16812768 | 2 |
| C2×#16812767 | 2 |
| #20295968 | 2 |
| #20295900 | 2 |
| C22⋊C8×D109 | 2 |
| #1854 | 109 |