Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#16812720 | C2 | semidirect |
| 2. #20295577 | C2 | semidirect |
| 3. C4×#13182028 | C2 | semidirect |
| 4. #20295251 | C2 | semidirect |
| 5. #20295243 | C2 | semidirect |
| 6. #20295233 | C2 | semidirect |
| 7. #20295227 | C2 | semidirect |
| 8. #20295221 | C2 | semidirect |
| 9. C4⋊C8×D109 | C2 | semidirect |
| 10. #20295021 | C2 | semidirect |
| 11. #461×C109 | C2 | semidirect |
| 47. #13182028 | D4 | semidirect |
| 136. C4×C109 | #135 | semidirect |
| 151. C109 | #3035 | semidirect |
| 158. #461 | D109 | semidirect |
| 292. C4 | #16812720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812720 | 2 |
| #20295577 | 2 |
| C4×#13182028 | 2 |
| #20295251 | 2 |
| #20295243 | 2 |
| #20295233 | 2 |
| #20295227 | 2 |
| #20295221 | 2 |
| C4⋊C8×D109 | 2 |
| #20295021 | 2 |
| #461×C109 | 2 |
| #3035 | 109 |