Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
3870 conjugacy classes of subgroups; only the 2232 normal subgroups are shown.
This group has 3870 conjugacy classes of subgroups — too many to draw. Only its 2232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C4⋊#1057 | C2 | direct (N × H) |
| 11. C2×C4⋊#1057 | C22 | direct (N × H) |
| 13. C23×C4×C13 | C8 | semidirect |
| 25. C4⋊#1057 | C23 | direct (N × H) |
| 31. C22×C4×C13 | C2×C8 | semidirect |
| 47. C23×C13 | C4⋊C8 | semidirect |
| 52. C2×C4×C13 | C22×C8 | semidirect |
| 70. C22×C13 | C2×C4⋊C8 | semidirect |
| 75. C4×C13 | C23×C8 | semidirect |
| 87. C23×C4 | #1057 | semidirect |
| 94. C2×C13 | C22×C4⋊C8 | semidirect |
| 109. C22×C4 | C2×#1057 | semidirect |
| 115. C13 | C23×C4⋊C8 | semidirect |
| 116. C23 | C4⋊#1057 | direct (N × H) |
| 128. C2×C4 | C22×#1057 | semidirect |
| 131. C22 | C2×C4⋊#1057 | direct (N × H) |
| 140. C4 | C23×#1057 | semidirect |
| 141. C2 | C22×C4⋊#1057 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#1057 | 2 |
| C22×C4⋊#1057 | 2 |
| C23×C4×Dic13 | 2 |
| C23×C4⋊C8 | 13 |