Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
472 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 197 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×D173 |
| commutator, socle, prime radical, cosocle | C23×C173 | C24 |
| Fitting | #384×C173 | C2 |
| hypercenter | #384 | D173 |
| hypocenter | C173 | #2859 |
| LCS | G ▷ C23×C173 ▷ C173 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 63. C4×C173 | #125 | semidirect |
| 74. C173 | #2859 | semidirect |
| 142. C4 | #19149670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149670 | 2 |
| #26011390 | 2 |
| #26011387 | 2 |
| #26011361 | 2 |
| #26011356 | 2 |
| C42×Dic173 | 2 |
| #384×C173 | 2 |
| #2859 | 173 |