Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
510 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 510 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 |
| 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×D8 | C2 | semidirect |
| 2. C2×C13×#127 | C2 | semidirect |
| 3. C2×C13×#102 | C2 | semidirect |
| 4. C13×#390 | C2 | semidirect |
| 5. C13×#336 | C2 | semidirect |
| 32. C2×D4×C13 | D4 | semidirect |
| 39. C2×C8×C13 | D4 | semidirect |
| 43. #2011 | C13 | direct (N × H) |
| 66. C2×C4×C13 | D8 | semidirect |
| 72. C22×D8 | C2×C13 | semidirect |
| 73. C2×#127 | C2×C13 | semidirect |
| 74. C2×#102 | C2×C13 | semidirect |
| 75. #390 | C2×C13 | semidirect |
| 76. #336 | C2×C13 | semidirect |
| 129. C2×D4 | D4×C13 | semidirect |
| 136. C2×C8 | D4×C13 | semidirect |
| 140. C13 | #2011 | direct (N × H) |
| 163. C2×C4 | C13×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×D8 | 2 |
| C2×C13×#127 | 2 |
| C2×C13×#102 | 2 |
| C13×#390 | 2 |
| C13×#336 | 2 |
| #2011 | 13 |