Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
356 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #382×C173 | C2 |
| hypercenter | #382 | D173 |
| hypocenter | C173 | #2844 |
| LCS | G ▷ C23×C173 ▷ C173 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 35. C42×C173 | Q8 | semidirect |
| 70. C173 | #2844 | semidirect |
| 106. C42 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011433 | 2 |
| #26011430 | 2 |
| #26011412 | 2 |
| #26011411 | 2 |
| #26011357 | 2 |
| #382×C173 | 2 |
| #2844 | 173 |