Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20295746 | C2 | semidirect |
| 3. #20295377 | C2 | semidirect |
| 4. #20295368 | C2 | semidirect |
| 5. #20295307 | C2 | semidirect |
| 6. #20295267 | C2 | semidirect |
| 7. #20295237 | C2 | semidirect |
| 8. #20295190 | C2 | semidirect |
| 9. C4×#13182018 | C2 | semidirect |
| 10. #20295023 | C2 | semidirect |
| 11. C8×D4×C109 | C2 | semidirect |
| 126. C109 | #3302 | semidirect |
| 136. C8×D4 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295746 | 2 |
| #20295681 | 2 |
| #20295377 | 2 |
| #20295368 | 2 |
| #20295307 | 2 |
| #20295267 | 2 |
| #20295237 | 2 |
| #20295190 | 2 |
| C4×#13182018 | 2 |
| #20295023 | 2 |
| C8×D4×C109 | 2 |
| #3302 | 109 |