Finite Group DatabasebetaFinite Group DatabasebetaOrder 28544.
158 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C223 | #99 |
| commutator | C23 | C42×C223 |
| Frattini, cosocle | C2×#41 | C22×C223 |
| socle | C2×C223 | #342 |
| prime radical | C2×#41×C223 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C223 ◁ C2×C4×C223 ◁ C2×#41×C223 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 52. C223 | #1392 | direct (N × H) |
| 53. #1392 | C223 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #413×C223 | 2 |
| #408×C223 | 2 |
| #1392 | 223 |