Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1640 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1640 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D13 |
| commutator, cosocle | C22×C13 | C25 |
| Frattini | C22 | C24×D13 |
| Fitting | C22×C13×C4⋊C4 | C2 |
| socle | C23×C13 | C24 |
| hypercenter | C22×C4⋊C4 | D13 |
| hypocenter | C13 | C2×#537 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6127 | C2 | semidirect |
| 2. C22×C13×C4⋊C4 | C2 | semidirect |
| 3. C2×#88184 | C2 | semidirect |
| 4. #11719215 | C2 | direct (N × H) |
| 5. C2×#88151 | C2 | semidirect |
| 6. C2×#88149 | C2 | semidirect |
| 11. C2×#6127 | C22 | semidirect |
| 17. C2×C13×C4⋊C4 | C22 | semidirect |
| 18. #88184 | C22 | semidirect |
| 21. #88151 | C22 | semidirect |
| 22. #88149 | C22 | semidirect |
| 26. C22×C4×C13 | D4 | semidirect |
| 59. C2×C4×C13 | C2×D4 | semidirect |
| 74. C22×C4⋊C4 | D13 | semidirect |
| 104. C2×C4⋊C4 | C2×D13 | semidirect |
| 107. C2×C13 | #537 | semidirect |
| 127. C22×C4 | D52 | semidirect |
| 135. C13 | C2×#537 | semidirect |
| 155. C2×C4 | C2×D52 | semidirect |
| 175. C2 | #11719215 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6127 | 2 |
| C22×C13×C4⋊C4 | 2 |
| C2×#88184 | 2 |
| #11719215 | 2 |
| C2×#88151 | 2 |
| C2×#88149 | 2 |
| C2×#537 | 13 |