Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
616 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×#16812661 | C2 | semidirect |
| 3. #20295108 | C2 | direct (N × H) |
| 4. C2×#16812619 | C2 | semidirect |
| 5. C2×C8×Dic109 | C2 | semidirect |
| 6. C2×#107×C109 | C2 | semidirect |
| 9. C2×D872 | C4 | semidirect |
| 13. #16812661 | C22 | semidirect |
| 16. #16812619 | C22 | semidirect |
| 17. C8×Dic109 | C22 | semidirect |
| 20. #107×C109 | C22 | semidirect |
| 24. C2×D436 | C2×C4 | semidirect |
| 30. D872 | C2×C4 | semidirect |
| 38. C2×C8×C109 | C2×C4 | semidirect |
| 54. C2×Dic109 | D8 | semidirect |
| 59. D436 | C22×C4 | semidirect |
| 61. C8×C109 | C22×C4 | semidirect |
| 76. Dic109 | C2×D8 | semidirect |
| 77. C2×C109 | C4×D8 | semidirect |
| 83. C109 | C2×C4×D8 | semidirect |
| 87. C2×#107 | D109 | semidirect |
| 101. #107 | C2×D109 | semidirect |
| 118. C2×C8 | C4×D109 | semidirect |
| 145. C8 | C2×C4×D109 | semidirect |
| 161. C2 | #20295108 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D872 | 2 |
| C2×#16812661 | 2 |
| #20295108 | 2 |
| C2×#16812619 | 2 |
| C2×C8×Dic109 | 2 |
| C2×#107×C109 | 2 |
| C2×C4×D8 | 109 |