Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
1008 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 210 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×D109⋊M16 | C2 | semidirect |
| 2. C2×#16812778 | C2 | semidirect |
| 3. #20296018 | C2 | direct (N × H) |
| 4. C2×#16812761 | C2 | semidirect |
| 8. D109⋊M16 | C22 | semidirect |
| 10. C2×D109⋊C8 | C22 | semidirect |
| 12. #16812778 | C22 | semidirect |
| 13. C2×C4⋊#89137 | C22 | semidirect |
| 16. #16812761 | C22 | semidirect |
| 18. C22×D436 | C4 | semidirect |
| 24. C2×D4×D109 | C4 | semidirect |
| 25. C2×D4×D109 | C4 | semidirect |
| 29. C22×D4×C109 | C4 | semidirect |
| 34. D109⋊C8 | C23 | semidirect |
| 37. C4⋊#89137 | C23 | semidirect |
| 50. C2×D436 | C2×C4 | semidirect |
| 63. D4×D109 | C2×C4 | semidirect |
| 78. C2×D4×C109 | C2×C4 | semidirect |
| 157. C2×C109 | #418 | semidirect |
| 161. D109 | #418 | semidirect |
| 164. C109 | C2×#418 | semidirect |
| 181. C22×D4 | #89137 | semidirect |
| 223. C2×D4 | C2×#89137 | semidirect |
| 325. C2 | #20296018 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D109⋊M16 | 2 |
| C2×#16812778 | 2 |
| #20296018 | 2 |
| C2×#16812761 | 2 |
| C22×D4×D109 | 2 |
| C2×#418 | 109 |