Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
1068 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 209 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×D103 |
| commutator, socle, cosocle | C23×C103 | C24 |
| Fitting | #379×C103 | C2 |
| prime radical | C25×C103 | C22 |
| hypercenter | #379 | D103 |
| hypocenter | C103 | #2848 |
| LCS | G ▷ C23×C103 ▷ C103 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#15692998 | C2 | semidirect |
| 3. #20267666 | C2 | semidirect |
| 4. #20267663 | C2 | semidirect |
| 5. #20267649 | C2 | semidirect |
| 8. C22×Dic206 | C22 | semidirect |
| 13. C2×C4⋊Dic103 | C22 | semidirect |
| 14. C2×Dic103⋊C4 | C22 | semidirect |
| 15. C2×Dic103⋊C4 | C22 | semidirect |
| 18. C103⋊#95 | C22 | semidirect |
| 39. C24×C103 | Q8 | semidirect |
| 71. C22×C103 | C22⋊Q8 | semidirect |
| 86. C103 | #2848 | semidirect |
| 110. C24 | Dic206 | semidirect |
| 157. C22 | #15692998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic103 | 2 |
| C2×#15692998 | 2 |
| #20267666 | 2 |
| #20267663 | 2 |
| #20267649 | 2 |
| #20267647 | 2 |
| #379×C103 | 2 |
| #2848 | 103 |