Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
272 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 124 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×C11 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C11 |
| Frattini, cosocle | C22×C4 | C23×C11 |
| prime radical | C23×C11 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 34. #1801 | C11 | direct (N × H) |
| 66. C4×C11 | #101 | semidirect |
| 103. C11 | #1801 | direct (N × H) |
| 131. C4 | C11×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Q8×C11 | 2 |
| C11×#423 | 2 |
| C2×C11×#101 | 2 |
| C11×#343 | 2 |
| #1801 | 11 |