Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
306 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 84 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 | C22×C4 | C23×C13 |
| prime radical | C13×#537 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C13×#104 | C2 | semidirect |
| 3. C13×#417 | C2 | semidirect |
| 4. C13×#384 | C2 | semidirect |
| 5. C13×#343 | C2 | semidirect |
| 40. C42×C13 | D4 | semidirect |
| 41. #2039 | C13 | direct (N × H) |
| 67. C2×#104 | C2×C13 | semidirect |
| 68. #417 | C2×C13 | semidirect |
| 69. #384 | C2×C13 | semidirect |
| 70. #343 | C2×C13 | semidirect |
| 125. C42 | D4×C13 | semidirect |
| 126. C13 | #2039 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#537 | 2 |
| C2×C13×#104 | 2 |
| C13×#417 | 2 |
| C13×#384 | 2 |
| C13×#343 | 2 |
| #2039 | 13 |