Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. C4×#13182030 | C2 | semidirect |
| 3. #20295139 | C2 | semidirect |
| 4. #20295137 | C2 | semidirect |
| 5. #20295133 | C2 | semidirect |
| 6. #20295129 | C2 | semidirect |
| 7. #20295124 | C2 | semidirect |
| 8. #20295061 | C2 | semidirect |
| 9. #20295021 | C2 | semidirect |
| 10. #97×D109 | C2 | semidirect |
| 11. #441×C109 | C2 | semidirect |
| 13. #16812722 | C4 | semidirect |
| 41. #13182030 | C2×C4 | semidirect |
| 49. #13182016 | C2×C4 | semidirect |
| 50. D872 | C2×C4 | semidirect |
| 54. C8×D109 | C2×C4 | semidirect |
| 65. Q16×C109 | C2×C4 | semidirect |
| 115. C109 | #2943 | semidirect |
| 121. #441 | D109 | semidirect |
| 165. Q16 | C4×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812722 | 2 |
| C4×#13182030 | 2 |
| #20295139 | 2 |
| #20295137 | 2 |
| #20295133 | 2 |
| #20295129 | 2 |
| #20295124 | 2 |
| #20295061 | 2 |
| #20295021 | 2 |
| #97×D109 | 2 |
| #441×C109 | 2 |
| #2943 | 109 |