Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
360 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 92 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. C42×#89137 | C2 | semidirect |
| 5. #20295898 | C2 | semidirect |
| 6. #20295897 | C2 | semidirect |
| 9. Q8×#89137 | C4 | semidirect |
| 11. D4×#89137 | C4 | semidirect |
| 18. #16812764 | C4 | semidirect |
| 19. #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 |
| 44. C4×#89137 | C2×C4 | semidirect |
| 58. #13182013 | C2×C4 | semidirect |
| 62. C4×Dic109 | C2×C4 | semidirect |
| 64. M16×C109 | C2×C4 | semidirect |
| 65. C42×C109 | C2×C4 | semidirect |
| 75. Q8×C109 | C42 | semidirect |
| 77. D4×C109 | C42 | semidirect |
| 88. D436 | C42 | semidirect |
| 98. Dic218 | C42 | semidirect |
| 112. #89137 | #104 | direct (N × H) |
| 128. C109 | C4×#104 | semidirect |
| 154. #104 | #89137 | direct (N × H) |
| 176. M16 | C2×#89137 | semidirect |
| 193. C42 | C2×#89137 | semidirect |
| 198. Q8 | C4×#89137 | semidirect |
| 205. D4 | C4×#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 |
| C42×#89137 | 2 |
| #20295898 | 2 |
| #20295897 | 2 |
| #104×D109 | 2 |
| C4×#104 | 109 |