Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 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×D29 |
| commutator, socle, cosocle | C22×C29 | C24 |
| Fitting | C29×C22⋊Q8 | C2 |
| hypercenter | C22⋊Q8 | D29 |
| hypocenter | C29 | #547 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#90809 | C2 | semidirect |
| 2. C2×#90805 | C2 | semidirect |
| 3. C29×C22⋊Q8 | C2 | semidirect |
| 4. #11745306 | C2 | semidirect |
| 5. C4×C22⋊D29 | C2 | semidirect |
| 6. #11745259 | C2 | semidirect |
| 7. #11745256 | C2 | semidirect |
| 8. #11745255 | C2 | semidirect |
| 9. C4⋊C4×D29 | C2 | semidirect |
| 10. #11745246 | C2 | semidirect |
| 11. #11745245 | C2 | semidirect |
| 53. D116 | D4 | semidirect |
| 76. Dic29 | #41 | semidirect |
| 90. C22⋊Q8 | D29 | semidirect |
| 95. C29 | #547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90809 | 2 |
| C2×#90805 | 2 |
| C29×C22⋊Q8 | 2 |
| #11745306 | 2 |
| C4×C22⋊D29 | 2 |
| #11745259 | 2 |
| #11745256 | 2 |
| #11745255 | 2 |
| C4⋊C4×D29 | 2 |
| #11745246 | 2 |
| #11745245 | 2 |
| #547 | 29 |