Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
360 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20295428 | C2 | semidirect |
| 3. #20295427 | C2 | semidirect |
| 4. #20295426 | C2 | semidirect |
| 5. #20295425 | C2 | semidirect |
| 9. #499×C109 | C2 | semidirect |
| 75. D109 | #499 | direct (N × H) |
| 77. C109 | C2×#499 | semidirect |
| 83. #499 | D109 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×D109 | 2 |
| #20295428 | 2 |
| #20295427 | 2 |
| #20295426 | 2 |
| #20295425 | 2 |
| #107×D109 | 2 |
| #106×D109 | 2 |
| C4×C8×D109 | 2 |
| #499×C109 | 2 |
| C2×#499 | 109 |