Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
390 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 108 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 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C13 |
| prime radical | C22×D4×C13 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C13×Q16 | C2 | semidirect |
| 4. C2×C13×#103 | C2 | semidirect |
| 6. C13×#391 | C2 | semidirect |
| 7. C13×#336 | C2 | semidirect |
| 64. #2015 | C13 | direct (N × H) |
| 102. C22×Q16 | C2×C13 | semidirect |
| 105. C2×#103 | C2×C13 | semidirect |
| 107. #391 | C2×C13 | semidirect |
| 108. #336 | C2×C13 | semidirect |
| 189. C13 | #2015 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×Q16 | 2 |
| C22×C13×SD16 | 2 |
| C2×C13×#124 | 2 |
| C2×C13×#103 | 2 |
| C2×C13×#102 | 2 |
| C13×#391 | 2 |
| C13×#336 | 2 |
| #2015 | 13 |