Finite Group DatabasebetaFinite Group DatabasebetaOrder 28544.
228 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 112 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×C223 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C223 |
| Frattini, cosocle | C22×C4 | C23×C223 |
| prime radical | C23×C223 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C223 ◁ C2×C42×C223 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 55. C223 | #1998 | direct (N × H) |
| 56. #1998 | C223 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#125×C223 | 2 |
| #423×C223 | 2 |
| C4×M16×C223 | 2 |
| #343×C223 | 2 |
| #1998 | 223 |