Finite Group DatabasebetaFinite Group DatabasebetaOrder 832.
260 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 91 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×#124 | C2 |
| hypercenter | #124 | D13 |
| hypocenter | C13 | H(3,𝔽4) |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#124 | C2 | semidirect |
| 2. #88201 | C2 | semidirect |
| 3. #88191 | C2 | semidirect |
| 4. #88139 | C2 | semidirect |
| 5. #88136 | C2 | semidirect |
| 6. #88129 | C2 | semidirect |
| 7. C23×D13 | C22 | semidirect |
| 8. C2×Q8×C13 | C22 | semidirect |
| 13. C2×Dic26 | C22 | semidirect |
| 14. C13×C22⋊C4 | C22 | semidirect |
| 15. C42×C13 | C22 | semidirect |
| 16. C22⋊Dic13 | C22 | semidirect |
| 17. #6103 | C22 | semidirect |
| 18. #6103 | C22 | semidirect |
| 19. #6103 | C22 | semidirect |
| 20. C4×Dic13 | C22 | semidirect |
| 50. #124 | D13 | semidirect |
| 59. C2×Q8 | C2×D13 | semidirect |
| 68. C22⋊C4 | C2×D13 | semidirect |
| 70. C42 | C2×D13 | semidirect |
| 71. C13 | H(3,𝔽4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#124 | 2 |
| #88201 | 2 |
| #88191 | 2 |
| #88139 | 2 |
| #88136 | 2 |
| #88129 | 2 |
| H(3,𝔽4) | 13 |