Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
402 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 158 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. #20296051 | C2 | semidirect |
| 2. #20296046 | C2 | semidirect |
| 3. #20296042 | C2 | semidirect |
| 4. #20296033 | C2 | semidirect |
| 7. #20295991 | C2 | semidirect |
| 11. #16812766 | C22 | semidirect |
| 12. C4⋊#11724786 | C22 | semidirect |
| 18. #16812754 | C22 | semidirect |
| 19. C4×#11724786 | C22 | semidirect |
| 111. C109 | #2924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296051 | 2 |
| #20296046 | 2 |
| #20296042 | 2 |
| #20296033 | 2 |
| #20295997 | 2 |
| D109⋊(C22⋊C8) | 2 |
| #20295991 | 2 |
| C2×#16812657 | 2 |
| #2924 | 109 |