Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
752 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 177 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×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting | C11×#390 | C2 |
| prime radical | C2×#66993 | C2 |
| hypercenter | #390 | D11 |
| hypocenter | C11 | #2858 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#66941 | C2 | semidirect |
| 3. C2×#66938 | C2 | semidirect |
| 4. C11×#390 | C2 | semidirect |
| 5. #10622834 | C2 | semidirect |
| 6. #10622601 | C2 | semidirect |
| 7. #10622570 | C2 | semidirect |
| 8. #10622552 | C2 | semidirect |
| 9. C42×Dic11 | C2 | semidirect |
| 62. C4×Dic11 | D4 | semidirect |
| 104. #390 | D11 | semidirect |
| 123. C4×C11 | #124 | semidirect |
| 126. Dic11 | #124 | semidirect |
| 188. C11 | #2858 | semidirect |
| 243. C4 | #66938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66993 | 2 |
| C2×#66941 | 2 |
| C2×#66938 | 2 |
| C11×#390 | 2 |
| #10622834 | 2 |
| #10622601 | 2 |
| #10622570 | 2 |
| #10622552 | 2 |
| C42×Dic11 | 2 |
| #2858 | 11 |