Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 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×D41 |
| commutator, socle, cosocle | C22×C41 | C24 |
| Fitting | C22⋊Q8×C41 | C2 |
| prime radical | C2×#10620306 | C2 |
| hypercenter | C22⋊Q8 | D41 |
| hypocenter | C41 | #536 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×D41 | C2 | semidirect |
| 3. #13050163 | C2 | semidirect |
| 4. #13050150 | C2 | semidirect |
| 5. #13050149 | C2 | semidirect |
| 6. #13050146 | C2 | semidirect |
| 7. #13050144 | C2 | semidirect |
| 8. #13050143 | C2 | semidirect |
| 9. #13050140 | C2 | semidirect |
| 10. #13050122 | C2 | semidirect |
| 11. C22⋊Q8×C41 | C2 | semidirect |
| 84. C41 | #536 | semidirect |
| 94. C22⋊Q8 | D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10620306 | 2 |
| C2×Q8×D41 | 2 |
| #13050163 | 2 |
| #13050150 | 2 |
| #13050149 | 2 |
| #13050146 | 2 |
| #13050144 | 2 |
| #13050143 | 2 |
| #13050140 | 2 |
| #13050122 | 2 |
| C22⋊Q8×C41 | 2 |
| #536 | 41 |