Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
578 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 214 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 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#3169 | C2 | semidirect |
| 2. C13×#2224 | C2 | semidirect |
| 3. C13×#2215 | C2 | semidirect |
| 4. C13×#2206 | C2 | semidirect |
| 5. C2×C13×C4⋊C16 | C2 | semidirect |
| 42. #33811 | C13 | direct (N × H) |
| 69. #3169 | C2×C13 | semidirect |
| 70. #2224 | C2×C13 | semidirect |
| 71. #2215 | C2×C13 | semidirect |
| 72. #2206 | C2×C13 | semidirect |
| 73. C2×C4⋊C16 | C2×C13 | semidirect |
| 87. C2×C4×C13 | D16 | semidirect |
| 176. C13 | #33811 | direct (N × H) |
| 190. C2×C4 | C13×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#3169 | 2 |
| C13×#2224 | 2 |
| C13×#2215 | 2 |
| C13×#2206 | 2 |
| C2×C13×C4⋊C16 | 2 |
| #33811 | 13 |