Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C13 |
| prime radical | C13×#547 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#500 | C2 | semidirect |
| 3. C13×#474 | C2 | semidirect |
| 4. C13×#461 | C2 | semidirect |
| 5. C13×#332 | C2 | semidirect |
| 6. C13×D4⋊C8 | C2 | semidirect |
| 7. C13×D4⋊C8 | C2 | semidirect |
| 50. #1647 | C13 | direct (N × H) |
| 78. #500 | C2×C13 | semidirect |
| 79. #474 | C2×C13 | semidirect |
| 80. #461 | C2×C13 | semidirect |
| 81. #332 | C2×C13 | semidirect |
| 82. D4⋊C8 | C2×C13 | semidirect |
| 83. D4⋊C8 | C2×C13 | semidirect |
| 147. C13 | #1647 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#547 | 2 |
| C13×#500 | 2 |
| C13×#474 | 2 |
| C13×#461 | 2 |
| C13×#332 | 2 |
| C13×D4⋊C8 | 2 |
| #1647 | 13 |