Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
568 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 228 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#261 |
| commutator, socle | C22×C13 | C23×C4 |
| Fitting | C4×Q8×C13 | C4 |
| prime radical, cosocle | C22×D13 | C24 |
| hypercenter | C4×Q8 | #261 |
| hypocenter | C13 | Q8×C4⋊C4 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. C4×Q8×C13 | C4 | semidirect |
| 14. Q8×Dic13 | C4 | semidirect |
| 16. #88141 | C4 | semidirect |
| 18. C4×Dic26 | C4 | semidirect |
| 32. C4⋊#261 | Q8 | direct (N × H) |
| 49. Q8×C13 | C4⋊C4 | semidirect |
| 62. Dic26 | C4⋊C4 | semidirect |
| 79. C4×C13 | C4×Q8 | semidirect |
| 82. Dic13 | C4×Q8 | semidirect |
| 88. C4×Q8 | #261 | semidirect |
| 125. C13 | Q8×C4⋊C4 | semidirect |
| 128. Q8 | C4⋊#261 | direct (N × H) |
| 161. C4 | Q8×#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#261 | 2 |
| C4×Q8×D13 | 2 |
| #11719083 | 2 |
| #11719059 | 2 |
| C4×C4⋊#261 | 2 |
| Q8×C4⋊C4 | 13 |