Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
484 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 162 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×#16812787 | C2 | semidirect |
| 2. C2×#16812786 | C2 | semidirect |
| 3. #20296058 | C2 | semidirect |
| 4. #20296055 | C2 | semidirect |
| 5. #20296030 | C2 | semidirect |
| 6. #20296001 | C2 | semidirect |
| 7. #20296000 | C2 | semidirect |
| 8. #20295985 | C2 | semidirect |
| 40. D109⋊C8 | D4 | semidirect |
| 116. C109 | #2932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812787 | 2 |
| C2×#16812786 | 2 |
| #20296058 | 2 |
| #20296055 | 2 |
| #20296030 | 2 |
| #20296001 | 2 |
| #20296000 | 2 |
| #20295985 | 2 |
| #20295575 | 2 |
| #2932 | 109 |