Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1770 conjugacy classes of subgroups; only the 542 normal subgroups are shown.
This group has 1770 conjugacy classes of subgroups — too many to draw. Only its 542 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C13 | C24 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C24 | C24×C13 |
| prime radical | C25×C13 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C13×#383 | C2 | semidirect |
| 3. C2×C43×C13 | C2 | semidirect |
| 5. C13×#1436 | C2 | semidirect |
| 8. C2×C13×#126 | C4 | semidirect |
| 38. #14711 | C13 | direct (N × H) |
| 62. C42×C13 | C22⋊C4 | semidirect |
| 64. C2×#383 | C2×C13 | semidirect |
| 65. C2×C43 | C2×C13 | semidirect |
| 67. #1436 | C2×C13 | semidirect |
| 91. C2×C4×C13 | #126 | semidirect |
| 94. C2×#126 | C4×C13 | semidirect |
| 166. C42 | C13×C22⋊C4 | semidirect |
| 167. C13 | #14711 | direct (N × H) |
| 191. C2×C4 | C13×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×#126 | 2 |
| C2×C13×#383 | 2 |
| C2×C43×C13 | 2 |
| C13×#1437 | 2 |
| C13×#1436 | 2 |
| #14711 | 13 |