Finite Group DatabasebetaFinite Group DatabasebetaOrder 832.
238 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D13 |
| commutator, socle, cosocle | C22×C13 | C24 |
| Fitting | C13×#123 | C2 |
| hypercenter | #123 | D13 |
| hypocenter | C13 | #553 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#123 | C2 | semidirect |
| 2. #88193 | C2 | semidirect |
| 3. #88192 | C2 | semidirect |
| 4. C4×C22⋊D13 | C2 | semidirect |
| 5. C4×C22⋊D13 | C2 | semidirect |
| 6. #88152 | C2 | semidirect |
| 7. #88147 | C2 | semidirect |
| 8. C4⋊C4×D13 | C2 | semidirect |
| 9. #88143 | C2 | semidirect |
| 10. #88138 | C2 | semidirect |
| 11. #88138 | C2 | semidirect |
| 12. #88137 | C2 | semidirect |
| 13. #88135 | C2 | semidirect |
| 14. #88133 | C2 | semidirect |
| 15. #88131 | C2 | semidirect |
| 107. #123 | D13 | semidirect |
| 160. C13 | #553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#123 | 2 |
| #88193 | 2 |
| #88192 | 2 |
| C4×C22⋊D13 | 2 |
| #88152 | 2 |
| #88147 | 2 |
| C4⋊C4×D13 | 2 |
| #88143 | 2 |
| #88138 | 2 |
| #88137 | 2 |
| #88135 | 2 |
| #88133 | 2 |
| #88131 | 2 |
| #553 | 13 |