Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
644 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 209 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 | C13×#384 | C2 |
| prime radical | C23×D13 | C23 |
| hypercenter | #384 | D13 |
| hypocenter | C13 | #2857 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#88123 | C2 | semidirect |
| 4. C13×#384 | C2 | semidirect |
| 6. #11718646 | C2 | semidirect |
| 7. #11718635 | C2 | semidirect |
| 35. C2×C4×D13 | Q8 | semidirect |
| 79. #384 | D13 | semidirect |
| 90. C2×D13 | C4⋊Q8 | semidirect |
| 93. C4×C13 | C22⋊Q8 | semidirect |
| 142. C13 | #2857 | semidirect |
| 184. C4 | #88151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88151 | 2 |
| C2×C42×D13 | 2 |
| C2×#88123 | 2 |
| C13×#384 | 2 |
| #11718648 | 2 |
| #11718646 | 2 |
| #11718635 | 2 |
| #2857 | 13 |