Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
160 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 48 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. Q16×#89137 | C2 | semidirect |
| 3. #20295952 | C2 | semidirect |
| 4. #20295939 | C2 | semidirect |
| 6. #20295913 | C2 | semidirect |
| 18. #16812644 | C4 | semidirect |
| 19. #16812643 | C4 | semidirect |
| 20. #16812642 | C4 | semidirect |
| 22. SD32×C109 | C4 | semidirect |
| 34. Dic436 | C2×C4 | semidirect |
| 39. #13182004 | C2×C4 | semidirect |
| 40. Q16×C109 | C2×C4 | semidirect |
| 42. C16×C109 | C2×C4 | semidirect |
| 79. C109 | #2175 | semidirect |
| 94. SD32 | #89137 | semidirect |
| 107. Q16 | C2×#89137 | semidirect |
| 121. C16 | C2×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#89137 | 2 |
| D8×#89137 | 2 |
| #20295952 | 2 |
| #20295939 | 2 |
| #20295938 | 2 |
| #20295913 | 2 |
| SD32×D109 | 2 |
| #2175 | 109 |