Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
444 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20295843 | C2 | semidirect |
| 2. #20295842 | C2 | semidirect |
| 3. #20295839 | C2 | semidirect |
| 4. #20295404 | C2 | semidirect |
| 5. #20295302 | C2 | semidirect |
| 6. #20295300 | C2 | semidirect |
| 7. #20295211 | C2 | semidirect |
| 8. #20295207 | C2 | semidirect |
| 9. #20295142 | C2 | semidirect |
| 10. #20295141 | C2 | semidirect |
| 11. #473×C109 | C2 | semidirect |
| 147. C109 | #3293 | semidirect |
| 154. #473 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295843 | 2 |
| #20295842 | 2 |
| #20295839 | 2 |
| #20295404 | 2 |
| #20295302 | 2 |
| #20295300 | 2 |
| #20295211 | 2 |
| #20295207 | 2 |
| #20295142 | 2 |
| #20295141 | 2 |
| #473×C109 | 2 |
| #3293 | 109 |