Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
584 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C11 |
| prime radical | C2×C11×#127 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C11×#125 | C2 | semidirect |
| 3. C11×#394 | C2 | semidirect |
| 4. C11×#390 | C2 | semidirect |
| 5. C11×#376 | C2 | semidirect |
| 30. #2641 | C11 | direct (N × H) |
| 46. C2×#125 | C2×C11 | semidirect |
| 47. #394 | C2×C11 | semidirect |
| 48. #390 | C2×C11 | semidirect |
| 49. #376 | C2×C11 | semidirect |
| 88. C11 | #2641 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#127 | 2 |
| C2×C11×#125 | 2 |
| C11×#394 | 2 |
| C11×#390 | 2 |
| C11×#376 | 2 |
| #2641 | 11 |