Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 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 | #384×C107 | C2 |
| prime radical | C22×D428 | C22 |
| hypercenter | #384 | D107 |
| hypocenter | C107 | #2823 |
| LCS | G ▷ C23×C107 ▷ C107 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16812103 | C2 | semidirect |
| 2. #20292557 | C2 | semidirect |
| 3. #20292549 | C2 | semidirect |
| 5. #384×C107 | C2 | semidirect |
| 29. C42×C107 | D4 | semidirect |
| 59. C107 | #2823 | semidirect |
| 64. #384 | D107 | semidirect |
| 88. C42 | D428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812103 | 2 |
| #20292557 | 2 |
| #20292549 | 2 |
| #20292544 | 2 |
| #384×C107 | 2 |
| #2823 | 107 |