Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
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×D181 |
| commutator, socle, prime radical, cosocle | C23×C181 | C24 |
| Fitting | #384×C181 | C2 |
| hypercenter | #384 | D181 |
| hypocenter | C181 | #2859 |
| LCS | G ▷ C23×C181 ▷ C181 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 63. C4×C181 | #125 | semidirect |
| 74. C181 | #2859 | semidirect |
| 142. C4 | #19153807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153807 | 2 |
| #26041178 | 2 |
| #26041175 | 2 |
| #26041149 | 2 |
| #26041144 | 2 |
| C42×Dic181 | 2 |
| #384×C181 | 2 |
| #2859 | 181 |