Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
340 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 340 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 | C22×C13 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×C4 | C23×C13 |
| prime radical | C2×C13×#121 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C13×C22⋊C8 | C2 | semidirect |
| 3. C13×#380 | C2 | semidirect |
| 4. C13×#327 | C2 | semidirect |
| 6. C22×D4×C13 | C4 | semidirect |
| 11. C13×#121 | C4 | semidirect |
| 14. C2×C13×C4⋊C4 | C4 | semidirect |
| 18. C13×C22⋊C8 | C22 | semidirect |
| 19. C13×#95 | C22 | semidirect |
| 46. #1519 | C13 | direct (N × H) |
| 80. C2×C22⋊C8 | C2×C13 | semidirect |
| 81. #380 | C2×C13 | semidirect |
| 82. #327 | C2×C13 | semidirect |
| 107. C22×D4 | C4×C13 | semidirect |
| 112. #121 | C4×C13 | semidirect |
| 115. C2×C4⋊C4 | C4×C13 | semidirect |
| 119. C22⋊C8 | C22×C13 | semidirect |
| 120. #95 | C22×C13 | semidirect |
| 155. C13 | #1519 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#121 | 2 |
| C2×C13×C22⋊C8 | 2 |
| C13×#380 | 2 |
| C13×#327 | 2 |
| #1519 | 13 |