Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
370 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 208 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×D4×C13 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×Q8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q82×C13 | C2 | semidirect |
| 3. C13×#498 | C2 | semidirect |
| 5. C13×#475 | C2 | semidirect |
| 6. C8×Q8×C13 | C2 | semidirect |
| 31. C13×SD16 | Q8 | direct (N × H) |
| 43. Q8×SD16 | C13 | direct (N × H) |
| 48. Q8×C13 | SD16 | direct (N × H) |
| 49. Q8×C13 | C2×Q8 | semidirect |
| 60. C8×C13 | C2×Q8 | semidirect |
| 61. Q82 | C2×C13 | semidirect |
| 63. #498 | C2×C13 | semidirect |
| 65. #475 | C2×C13 | semidirect |
| 66. C8×Q8 | C2×C13 | semidirect |
| 106. SD16 | Q8×C13 | direct (N × H) |
| 118. C13 | Q8×SD16 | direct (N × H) |
| 123. Q8 | C13×SD16 | direct (N × H) |
| 124. Q8 | C2×Q8×C13 | semidirect |
| 135. C8 | C2×Q8×C13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q82×C13 | 2 |
| D4×Q8×C13 | 2 |
| C13×#498 | 2 |
| C13×#476 | 2 |
| C13×#475 | 2 |
| C8×Q8×C13 | 2 |
| C4×C13×SD16 | 2 |
| Q8×SD16 | 13 |