Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
362 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #20294922 | C2 | semidirect |
| 5. #20294788 | C2 | semidirect |
| 6. #20294780 | C2 | semidirect |
| 7. C2×#106×C109 | C2 | semidirect |
| 17. #16812621 | C4 | semidirect |
| 41. C4⋊Dic109 | C2×C4 | semidirect |
| 51. C2×C8×C109 | C2×C4 | semidirect |
| 88. D436 | C4⋊C4 | semidirect |
| 124. C109 | #1864 | semidirect |
| 126. C2×#106 | D109 | semidirect |
| 169. C2×C8 | C4×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812661 | 2 |
| C2×#16812621 | 2 |
| C2×#16812619 | 2 |
| #20294922 | 2 |
| #20294788 | 2 |
| #20294780 | 2 |
| C2×#106×C109 | 2 |
| #1864 | 109 |