Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
456 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 173 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. #20294921 | C2 | semidirect |
| 4. #20294907 | C2 | semidirect |
| 6. #20294894 | C2 | semidirect |
| 7. #384×C109 | C2 | semidirect |
| 9. #16812693 | C4 | semidirect |
| 28. #13182008 | C2×C4 | semidirect |
| 37. C42×C109 | C2×C4 | semidirect |
| 73. C109 | #2383 | semidirect |
| 79. #384 | D109 | semidirect |
| 110. C42 | C4×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812693 | 2 |
| #20294921 | 2 |
| #20294916 | 2 |
| #20294907 | 2 |
| #20294897 | 2 |
| #20294894 | 2 |
| #384×C109 | 2 |
| #2383 | 109 |