Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
460 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 110 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 | C2×#99 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C13 |
| prime radical | C22×D4×C13 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C13×#1324 | C2 | semidirect |
| 4. C13×#1319 | C2 | semidirect |
| 43. #11531 | C13 | direct (N × H) |
| 48. C2×Q8×C13 | M16 | semidirect |
| 80. C42×C13 | M16 | semidirect |
| 83. #1324 | C2×C13 | semidirect |
| 84. #1319 | C2×C13 | semidirect |
| 188. C2×Q8 | C13×M16 | semidirect |
| 220. C42 | C13×M16 | semidirect |
| 221. C13 | #11531 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×#124 | 2 |
| C13×#1465 | 2 |
| C13×#1324 | 2 |
| C13×#1319 | 2 |
| #11531 | 13 |