Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
418 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 418 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. #20295761 | C2 | semidirect |
| 2. #20295413 | C2 | semidirect |
| 3. #20295402 | C2 | semidirect |
| 4. #20295241 | C2 | semidirect |
| 5. #20295223 | C2 | semidirect |
| 6. #20295221 | C2 | semidirect |
| 7. #20295218 | C2 | semidirect |
| 8. #20295157 | C2 | semidirect |
| 9. #20295136 | C2 | semidirect |
| 10. C4×#13182017 | C2 | semidirect |
| 11. #550×C109 | C2 | semidirect |
| 108. #11724784 | #41 | semidirect |
| 135. C109 | #3399 | semidirect |
| 137. #550 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295761 | 2 |
| #20295413 | 2 |
| #20295402 | 2 |
| #20295241 | 2 |
| #20295223 | 2 |
| #20295221 | 2 |
| #20295218 | 2 |
| #20295157 | 2 |
| #20295136 | 2 |
| C4×#13182017 | 2 |
| #550×C109 | 2 |
| #3399 | 109 |