Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
196 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×#261 |
| commutator, socle | C2×C13 | C2×C4×C8 |
| Fitting | C13×M32 | C4 |
| prime radical | C22×D13 | C2×C8 |
| cosocle | C8×D13 | C23 |
| hypercenter | M32 | #261 |
| hypocenter | C13 | C4×M32 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C8 ◁ M32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11718216 | C2 | semidirect |
| 5. C16×#261 | C2 | semidirect |
| 9. #88106 | C4 | semidirect |
| 14. #88098 | C4 | semidirect |
| 16. C13×M32 | C4 | semidirect |
| 17. #88052 | C4 | semidirect |
| 18. #88038 | C4 | semidirect |
| 35. #6092 | C2×C4 | semidirect |
| 36. C13×C16 | C2×C4 | semidirect |
| 37. #6090 | C2×C4 | semidirect |
| 65. #261 | M32 | direct (N × H) |
| 77. M32 | #261 | direct (N × H) |
| 105. C16 | C2×#261 | semidirect |
| 106. C13 | C4×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#261 | 2 |
| D13⋊M32 | 2 |
| D13×M32 | 2 |
| #11718216 | 2 |
| C16×#261 | 2 |
| C4×M32 | 13 |