Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1134 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 165 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 | C2×C13×#123 | C2 |
| hypercenter | C2×#123 | D13 |
| hypocenter | C13 | #2613 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×#123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D52 | C2 | semidirect |
| 2. C2×C13×#123 | C2 | semidirect |
| 3. C2×#88191 | C2 | semidirect |
| 4. #11718872 | C2 | semidirect |
| 5. #11718652 | C2 | semidirect |
| 6. #11718621 | C2 | semidirect |
| 7. #11718616 | C2 | semidirect |
| 11. C22×C22⋊D13 | C22 | semidirect |
| 16. C2×C13×C4⋊C4 | C22 | semidirect |
| 18. C2×C13×C22⋊C4 | C22 | semidirect |
| 21. C2×#6103 | C22 | semidirect |
| 22. C2×#6103 | C22 | semidirect |
| 23. #88071 | C22 | semidirect |
| 29. C23×D13 | D4 | semidirect |
| 34. C22×C4×C13 | D4 | semidirect |
| 80. C2×#123 | D13 | semidirect |
| 114. C2×C4⋊C4 | C2×D13 | semidirect |
| 119. C2×C22⋊C4 | C2×D13 | semidirect |
| 143. C22×C4 | C22⋊D13 | semidirect |
| 153. C13 | #2613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D52 | 2 |
| C2×C13×#123 | 2 |
| C2×#88191 | 2 |
| #11718872 | 2 |
| #11718652 | 2 |
| #11718621 | 2 |
| #11718616 | 2 |
| #2613 | 13 |