Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
474 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C13 |
| prime radical | C2×C13×#127 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C13×SD16 | C2 | semidirect |
| 3. C2×C13×#102 | C2 | semidirect |
| 4. C13×#391 | C2 | semidirect |
| 5. C13×#336 | C2 | semidirect |
| 22. C2×Q8×C13 | D4 | semidirect |
| 39. C2×C8×C13 | D4 | semidirect |
| 42. #2014 | C13 | direct (N × H) |
| 63. C2×C4×C13 | SD16 | semidirect |
| 69. C22×SD16 | C2×C13 | semidirect |
| 71. C2×#102 | C2×C13 | semidirect |
| 72. #391 | C2×C13 | semidirect |
| 73. #336 | C2×C13 | semidirect |
| 111. C2×Q8 | D4×C13 | semidirect |
| 128. C2×C8 | D4×C13 | semidirect |
| 131. C13 | #2014 | direct (N × H) |
| 152. C2×C4 | C13×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×SD16 | 2 |
| C2×C13×#127 | 2 |
| C2×C13×#102 | 2 |
| C13×#391 | 2 |
| C13×#336 | 2 |
| #2014 | 13 |