Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
612 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting, prime radical | C2×C13×#127 | C2 |
| hypercenter | C2×#127 | D13 |
| hypocenter | C13 | #2709 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#88189 | C2 | semidirect |
| 3. #11718883 | C2 | semidirect |
| 4. #11718883 | C2 | semidirect |
| 5. #11718883 | C2 | semidirect |
| 6. #11718881 | C2 | semidirect |
| 7. #11718881 | C2 | semidirect |
| 8. #11718881 | C2 | semidirect |
| 9. #11718594 | C2 | semidirect |
| 218. C13 | #2709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#127 | 2 |
| C2×#88189 | 2 |
| #11718883 | 2 |
| #11718881 | 2 |
| #11718594 | 2 |
| #2709 | 13 |