Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20295841 | C2 | semidirect |
| 2. #20295840 | C2 | semidirect |
| 3. #20295404 | C2 | semidirect |
| 4. #20295301 | C2 | semidirect |
| 5. #20295299 | C2 | semidirect |
| 6. #20295298 | C2 | semidirect |
| 7. #20295209 | C2 | semidirect |
| 8. #20295207 | C2 | semidirect |
| 9. #20295143 | C2 | semidirect |
| 10. #20295141 | C2 | semidirect |
| 11. #578×C109 | C2 | semidirect |
| 147. C109 | #3293 | semidirect |
| 150. #578 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295841 | 2 |
| #20295840 | 2 |
| #20295404 | 2 |
| #20295301 | 2 |
| #20295299 | 2 |
| #20295298 | 2 |
| #20295209 | 2 |
| #20295207 | 2 |
| #20295143 | 2 |
| #20295141 | 2 |
| #578×C109 | 2 |
| #3293 | 109 |