Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
820 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 237 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. C22×C4⋊Dic109 | C2 | semidirect |
| 4. #20294953 | C2 | direct (N × H) |
| 5. C2×#16812606 | C2 | semidirect |
| 6. C2×#95×C109 | C2 | semidirect |
| 11. C2×C4⋊Dic109 | C22 | semidirect |
| 16. #16812606 | C22 | semidirect |
| 19. #95×C109 | C22 | semidirect |
| 94. C2×C109 | #397 | semidirect |
| 102. C109 | C2×#397 | semidirect |
| 108. C2×#95 | D109 | semidirect |
| 121. #95 | C2×D109 | semidirect |
| 197. C2 | #20294953 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic109 | 2 |
| C22×#13182006 | 2 |
| #20294953 | 2 |
| C2×#16812606 | 2 |
| C2×#95×C109 | 2 |
| C2×#397 | 109 |