Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. #20295577 | C2 | semidirect |
| 2. #20295403 | C2 | semidirect |
| 3. #20295374 | C2 | semidirect |
| 4. #20295263 | C2 | semidirect |
| 5. #20295108 | C2 | semidirect |
| 6. C4×C8×D109 | C2 | semidirect |
| 7. #500×C109 | C2 | semidirect |
| 63. C4×D109 | D8 | semidirect |
| 64. C8×C109 | #41 | semidirect |
| 86. C109 | #3169 | semidirect |
| 88. #500 | D109 | semidirect |
| 151. C8 | #13182030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295577 | 2 |
| #20295403 | 2 |
| #20295374 | 2 |
| #20295263 | 2 |
| #20295108 | 2 |
| C4×C8×D109 | 2 |
| #500×C109 | 2 |
| #3169 | 109 |