Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
366 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1619 |
| commutator, Frattini, cosocle | C4×C8 | C23×C11 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C4×C8×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#3293 | C2 | semidirect |
| 2. C11×#2213 | C2 | semidirect |
| 3. C11×#1709 | C2 | semidirect |
| 4. C11×#1358 | C2 | semidirect |
| 5. C11×#1335 | C2 | semidirect |
| 37. #12311 | C11 | direct (N × H) |
| 62. #3293 | C2×C11 | semidirect |
| 63. #2213 | C2×C11 | semidirect |
| 64. #1709 | C2×C11 | semidirect |
| 65. #1358 | C2×C11 | semidirect |
| 66. #1335 | C2×C11 | semidirect |
| 152. C11 | #12311 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#3293 | 2 |
| C11×#2213 | 2 |
| C11×#1709 | 2 |
| C11×#1358 | 2 |
| C11×#1335 | 2 |
| #12311 | 11 |