Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
378 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 168 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C13 |
| prime radical | C2×C13×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C13×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×#485 | C2 | semidirect |
| 3. C13×#470 | C2 | semidirect |
| 4. C13×#467 | C2 | semidirect |
| 5. C13×#451 | C2 | semidirect |
| 50. #3202 | C13 | direct (N × H) |
| 72. #485 | C2×C13 | semidirect |
| 73. #470 | C2×C13 | semidirect |
| 74. #467 | C2×C13 | semidirect |
| 75. #451 | C2×C13 | semidirect |
| 135. C13 | #3202 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#536 | 2 |
| C13×#485 | 2 |
| C13×#470 | 2 |
| C13×#467 | 2 |
| C13×#451 | 2 |
| C13×#408 | 2 |
| #3202 | 13 |