Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
388 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 98 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. C2×#16812753 | C2 | semidirect |
| 4. C4⋊C4×#89137 | C2 | semidirect |
| 5. #20295900 | C2 | semidirect |
| 6. #20295899 | C2 | semidirect |
| 11. D4×#89137 | C4 | semidirect |
| 17. #16812761 | C4 | semidirect |
| 23. #16812621 | C4 | semidirect |
| 24. #16812620 | C4 | semidirect |
| 25. #16812619 | C4 | semidirect |
| 26. #102×C109 | C4 | semidirect |
| 35. D109⋊C8 | C2×C4 | semidirect |
| 40. C4⋊#89137 | C2×C4 | semidirect |
| 54. C2×#11724784 | C2×C4 | semidirect |
| 57. C4⋊Dic109 | C2×C4 | semidirect |
| 60. C2×C8×C109 | C2×C4 | semidirect |
| 61. C4⋊C4×C109 | C2×C4 | semidirect |
| 85. D4×C109 | C42 | semidirect |
| 93. D436 | C42 | semidirect |
| 140. C109 | #1762 | semidirect |
| 164. #102 | #89137 | semidirect |
| 190. C2×C8 | C2×#89137 | semidirect |
| 197. C4⋊C4 | C2×#89137 | semidirect |
| 216. D4 | C4×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#89137 | 2 |
| C2×#16812761 | 2 |
| C2×#16812753 | 2 |
| C4⋊C4×#89137 | 2 |
| #20295900 | 2 |
| #20295899 | 2 |
| #102×D109 | 2 |
| #1762 | 109 |