Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
310 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#537 | C2 | semidirect |
| 2. C13×#447 | C2 | semidirect |
| 3. C13×#394 | C2 | semidirect |
| 4. C13×#327 | C2 | semidirect |
| 5. C13×#324 | C2 | semidirect |
| 43. #1598 | C13 | direct (N × H) |
| 71. C2×C4×C13 | D8 | semidirect |
| 74. #537 | C2×C13 | semidirect |
| 75. #447 | C2×C13 | semidirect |
| 76. #394 | C2×C13 | semidirect |
| 77. #327 | C2×C13 | semidirect |
| 78. #324 | C2×C13 | semidirect |
| 143. C13 | #1598 | direct (N × H) |
| 171. C2×C4 | C13×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#537 | 2 |
| C13×#447 | 2 |
| C13×#394 | 2 |
| C13×#327 | 2 |
| C13×#324 | 2 |
| #1598 | 13 |