Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
752 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting | C43×C11 | C2 |
| prime radical | C2×#66927 | C2 |
| hypercenter | C43 | D11 |
| hypocenter | C11 | #2858 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#66928 | C2 | semidirect |
| 3. C2×#66922 | C2 | semidirect |
| 4. C43×C11 | C2 | semidirect |
| 5. #10622552 | C2 | semidirect |
| 30. C42×C11 | D4 | semidirect |
| 53. C43 | D11 | semidirect |
| 61. C4×C11 | #124 | semidirect |
| 94. C42 | D44 | semidirect |
| 95. C11 | #2858 | semidirect |
| 120. C4 | #66928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66928 | 2 |
| C2×#66927 | 2 |
| C2×#66922 | 2 |
| C43×C11 | 2 |
| #10622552 | 2 |
| #2858 | 11 |