Finite Group DatabasebetaFinite Group DatabasebetaOrder 832.
294 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 103 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×#121 | C2 |
| hypercenter | #121 | D13 |
| hypocenter | C13 | #537 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6129 | C2 | semidirect |
| 2. C2×#6127 | C2 | semidirect |
| 3. C13×#121 | C2 | semidirect |
| 4. #88193 | C2 | semidirect |
| 5. #88192 | C2 | semidirect |
| 6. #88192 | C2 | semidirect |
| 7. #88178 | C2 | semidirect |
| 8. #88151 | C2 | semidirect |
| 9. C4⋊C4×D13 | C2 | semidirect |
| 10. #88138 | C2 | semidirect |
| 11. #88132 | C2 | semidirect |
| 59. C4×D13 | D4 | semidirect |
| 92. #121 | D13 | semidirect |
| 126. C13 | #537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6129 | 2 |
| C2×#6127 | 2 |
| C13×#121 | 2 |
| #88193 | 2 |
| #88192 | 2 |
| #88178 | 2 |
| #88151 | 2 |
| C4⋊C4×D13 | 2 |
| #88138 | 2 |
| #88132 | 2 |
| #537 | 13 |