Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
582 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C13 |
| prime radical | C22×D4×C13 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×#126 | C2 | semidirect |
| 2. C22×C42×C13 | C2 | semidirect |
| 3. C13×#388 | C2 | semidirect |
| 4. C13×#387 | C2 | semidirect |
| 6. C13×#385 | C2 | semidirect |
| 7. C13×#383 | C2 | semidirect |
| 40. C42×C13 | D4 | semidirect |
| 41. #2852 | C13 | direct (N × H) |
| 64. C2×#126 | C2×C13 | semidirect |
| 65. C22×C42 | C2×C13 | semidirect |
| 66. #388 | C2×C13 | semidirect |
| 67. #387 | C2×C13 | semidirect |
| 69. #385 | C2×C13 | semidirect |
| 70. #383 | C2×C13 | semidirect |
| 76. C22×C13 | #126 | semidirect |
| 122. C42 | D4×C13 | semidirect |
| 123. C13 | #2852 | direct (N × H) |
| 151. C22 | C13×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#126 | 2 |
| C22×C42×C13 | 2 |
| C13×#388 | 2 |
| C13×#387 | 2 |
| C13×#386 | 2 |
| C13×#385 | 2 |
| C13×#383 | 2 |
| #2852 | 13 |