Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
528 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 234 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×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×D16 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×Q8×C13 ◁ C8×Q8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×C13×D8 | C2 | semidirect |
| 2. C13×#2252 | C2 | semidirect |
| 3. C13×#2224 | C2 | semidirect |
| 4. Q8×C13×C16 | C2 | semidirect |
| 23. C13×D16 | Q8 | direct (N × H) |
| 31. Q8×D16 | C13 | direct (N × H) |
| 38. C13×D8 | C2×Q8 | semidirect |
| 47. C13×C16 | C2×Q8 | semidirect |
| 48. Q8×D8 | C2×C13 | semidirect |
| 49. #2252 | C2×C13 | semidirect |
| 50. #2224 | C2×C13 | semidirect |
| 51. Q8×C16 | C2×C13 | semidirect |
| 55. Q8×C13 | D16 | direct (N × H) |
| 92. D16 | Q8×C13 | direct (N × H) |
| 110. D8 | C2×Q8×C13 | semidirect |
| 119. C16 | C2×Q8×C13 | semidirect |
| 120. C13 | Q8×D16 | direct (N × H) |
| 123. Q8 | C13×D16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C13×D8 | 2 |
| C13×#2252 | 2 |
| C13×#2224 | 2 |
| Q8×C13×C16 | 2 |
| C4×C13×D16 | 2 |
| Q8×D16 | 13 |