Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 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×#16812728 | C2 | semidirect |
| 3. C4×Q8×D109 | C2 | semidirect |
| 4. #20295247 | C2 | semidirect |
| 5. #20295246 | C2 | semidirect |
| 6. #20295237 | C2 | semidirect |
| 7. #20295236 | C2 | semidirect |
| 8. #20295223 | C2 | semidirect |
| 9. #20295048 | C2 | semidirect |
| 10. #20295024 | C2 | semidirect |
| 11. #460×C109 | C2 | semidirect |
| 50. Q8×D109 | D4 | semidirect |
| 132. C4×C109 | #137 | semidirect |
| 147. C109 | #3037 | semidirect |
| 156. #460 | D109 | semidirect |
| 285. C4 | #16812728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812728 | 2 |
| #20295574 | 2 |
| C4×Q8×D109 | 2 |
| #20295247 | 2 |
| #20295246 | 2 |
| #20295237 | 2 |
| #20295236 | 2 |
| #20295223 | 2 |
| #20295048 | 2 |
| #20295024 | 2 |
| #460×C109 | 2 |
| #3037 | 109 |