Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
712 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D107 |
| commutator, socle, cosocle | C23×C107 | C24 |
| Fitting | #379×C107 | C2 |
| hypercenter | #379 | D107 |
| hypocenter | C107 | #2812 |
| LCS | G ▷ C23×C107 ▷ C107 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16812078 | C2 | semidirect |
| 2. #20292552 | C2 | semidirect |
| 3. #20292543 | C2 | semidirect |
| 4. #20292536 | C2 | semidirect |
| 5. #379×C107 | C2 | semidirect |
| 6. C22×D428 | C22 | semidirect |
| 9. C2×C4⋊Dic107 | C22 | semidirect |
| 11. C2×(C2×D107)⋊C4 | C22 | semidirect |
| 12. C107⋊#95 | C22 | semidirect |
| 13. C107⋊#95 | C22 | semidirect |
| 28. C24×C107 | D4 | semidirect |
| 75. C107 | #2812 | semidirect |
| 80. #379 | D107 | semidirect |
| 95. C24 | D428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812078 | 2 |
| #20292552 | 2 |
| #20292543 | 2 |
| #20292536 | 2 |
| #379×C107 | 2 |
| #2812 | 107 |