Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
420 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 119 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 | #399×C107 | C2 |
| prime radical | C22×C22⋊D107 | C22 |
| hypercenter | #399 | D107 |
| hypocenter | C107 | #2801 |
| LCS | G ▷ C23×C107 ▷ C107 | |
| UCS | C1 ◁ C23 ◁ #399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C107⋊#401 | C2 | semidirect |
| 2. #20292551 | C2 | semidirect |
| 4. #20292522 | C2 | semidirect |
| 5. #20292517 | C2 | semidirect |
| 6. #20292515 | C2 | semidirect |
| 7. #399×C107 | C2 | semidirect |
| 78. C107 | #2801 | semidirect |
| 80. #399 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C107⋊#401 | 2 |
| #20292551 | 2 |
| #20292542 | 2 |
| #20292522 | 2 |
| #20292517 | 2 |
| #20292515 | 2 |
| #399×C107 | 2 |
| #2801 | 107 |