Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
320 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. M16×#89137 | C2 | semidirect |
| 4. #20295962 | C2 | semidirect |
| 5. #20295898 | C2 | semidirect |
| 6. #20295897 | C2 | semidirect |
| 9. Q8×#89137 | C4 | semidirect |
| 11. D4×#89137 | C4 | semidirect |
| 17. #16812764 | C4 | semidirect |
| 18. #16812763 | C4 | semidirect |
| 25. #16812627 | C4 | semidirect |
| 26. #16812626 | C4 | semidirect |
| 27. #16812625 | C4 | semidirect |
| 28. #104×C109 | C4 | semidirect |
| 32. #13182039 | C2×C4 | semidirect |
| 43. C4×#89137 | C2×C4 | semidirect |
| 57. #13182013 | C2×C4 | semidirect |
| 61. C4×Dic109 | C2×C4 | semidirect |
| 63. M16×C109 | C2×C4 | semidirect |
| 64. C42×C109 | C2×C4 | semidirect |
| 127. C109 | #1759 | semidirect |
| 152. #104 | #89137 | semidirect |
| 175. M16 | C2×#89137 | semidirect |
| 191. C42 | C2×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#89137 | 2 |
| D109⋊#104 | 2 |
| M16×#89137 | 2 |
| #20295962 | 2 |
| #20295898 | 2 |
| #20295897 | 2 |
| #104×D109 | 2 |
| #1759 | 109 |