Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
284 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 70 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. #20296045 | C2 | semidirect |
| 2. C4×C4⋊#89137 | C2 | semidirect |
| 3. #20295878 | C2 | semidirect |
| 12. #16812696 | C4 | semidirect |
| 17. #16812661 | C4 | semidirect |
| 19. C4⋊Q8×C109 | C4 | semidirect |
| 90. C109 | #1502 | semidirect |
| 96. C4⋊Q8 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296045 | 2 |
| C4×C4⋊#89137 | 2 |
| #20295878 | 2 |
| #20295577 | 2 |
| #1502 | 109 |