Finite Group DatabasebetaFinite Group DatabasebetaOrder 832.
290 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 105 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×C22⋊Q8 | C2 |
| hypercenter | C22⋊Q8 | D13 |
| hypocenter | C13 | #548 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×D13 | C2 | semidirect |
| 2. C2×#6127 | C2 | semidirect |
| 3. C13×C22⋊Q8 | C2 | semidirect |
| 4. #88201 | C2 | semidirect |
| 5. C4×C22⋊D13 | C2 | semidirect |
| 6. #88150 | C2 | semidirect |
| 7. #88149 | C2 | semidirect |
| 8. #88147 | C2 | semidirect |
| 9. #88141 | C2 | semidirect |
| 10. #88139 | C2 | semidirect |
| 11. #88138 | C2 | semidirect |
| 58. Dic26 | D4 | semidirect |
| 69. C2×D13 | #41 | semidirect |
| 83. C22⋊Q8 | D13 | semidirect |
| 120. C13 | #548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D13 | 2 |
| C2×#6127 | 2 |
| C13×C22⋊Q8 | 2 |
| #88201 | 2 |
| C4×C22⋊D13 | 2 |
| #88150 | 2 |
| #88149 | 2 |
| #88147 | 2 |
| #88141 | 2 |
| #88139 | 2 |
| #88138 | 2 |
| #548 | 13 |