Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
852 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 181 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, prime radical | C2×#121×C107 | C2 |
| hypercenter | C2×#121 | D107 |
| hypocenter | C107 | #2436 |
| LCS | G ▷ C23×C107 ▷ C107 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic214 | C2 | semidirect |
| 2. C2×#16812096 | C2 | semidirect |
| 3. #20292539 | C2 | semidirect |
| 4. #20292532 | C2 | semidirect |
| 5. #20292507 | C2 | semidirect |
| 6. C4×C22⋊Dic107 | C2 | semidirect |
| 30. C2×Dic214 | D4 | semidirect |
| 85. C22×C107 | #124 | semidirect |
| 102. C107 | #2436 | semidirect |
| 187. C22 | #16812096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic214 | 2 |
| C2×#16812096 | 2 |
| #20292539 | 2 |
| #20292532 | 2 |
| #20292507 | 2 |
| C4×C22⋊Dic107 | 2 |
| C2×#121×C107 | 2 |
| #2436 | 107 |