Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. C2×C42×D109 | C2 | semidirect |
| 3. C2×#16812627 | C2 | semidirect |
| 4. C2×#16812625 | C2 | semidirect |
| 5. #20294989 | C2 | semidirect |
| 6. #20294785 | C2 | semidirect |
| 7. #339×C109 | C2 | semidirect |
| 13. #16812679 | C4 | semidirect |
| 14. #16812674 | C4 | semidirect |
| 32. C2×Dic218 | C2×C4 | semidirect |
| 34. C2×D436 | C2×C4 | semidirect |
| 55. C4×Dic109 | D4 | semidirect |
| 61. C4⋊C4×C109 | C2×C4 | semidirect |
| 65. C42×C109 | D4 | semidirect |
| 113. C2×D109 | #104 | semidirect |
| 130. C109 | #1896 | semidirect |
| 137. #339 | D109 | semidirect |
| 186. C4⋊C4 | C4×D109 | semidirect |
| 195. C42 | D436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295538 | 2 |
| C2×C42×D109 | 2 |
| C2×#16812627 | 2 |
| C2×#16812625 | 2 |
| #20294989 | 2 |
| #20294785 | 2 |
| #339×C109 | 2 |
| #1896 | 109 |