Finite Group DatabasebetaFinite Group DatabasebetaOrder 33344.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 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×D521 |
| commutator, socle, cosocle | C22×C521 | C24 |
| Fitting | #125×C521 | C2 |
| prime radical | C2×D2084 | C22 |
| hypercenter | #125 | D521 |
| hypocenter | C521 | #554 |
| LCS | G ▷ C22×C521 ▷ C521 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30659707 | C2 | semidirect |
| 2. #30659699 | C2 | semidirect |
| 3. #30659688 | C2 | semidirect |
| 4. #30659686 | C2 | semidirect |
| 5. #30659686 | C2 | semidirect |
| 6. C4×Dic1042 | C2 | semidirect |
| 10. C4⋊C4×D521 | C2 | semidirect |
| 11. #125×C521 | C2 | semidirect |
| 38. D2084 | Q8 | semidirect |
| 70. C521 | #554 | semidirect |
| 74. #125 | D521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30659707 | 2 |
| #30659699 | 2 |
| #30659688 | 2 |
| #30659686 | 2 |
| C4×Dic1042 | 2 |
| C4×D2084 | 2 |
| #30659670 | 2 |
| C4⋊C4×D521 | 2 |
| #125×C521 | 2 |
| #554 | 521 |