Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
348 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C181 | #392 |
| commutator, Frattini, cosocle | C22×C4 | C23×C181 |
| prime radical | #575×C181 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C181 ◁ C22×C4×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#137×C181 | C2 | semidirect |
| 3. #536×C181 | C2 | semidirect |
| 4. #421×C181 | C2 | semidirect |
| 5. #419×C181 | C2 | semidirect |
| 6. #410×C181 | C2 | semidirect |
| 7. #344×C181 | C2 | semidirect |
| 136. C181 | #2009 | direct (N × H) |
| 137. #2009 | C181 | direct (N × H) |
| 139. C2×#137 | C2×C181 | semidirect |
| 140. #536 | C2×C181 | semidirect |
| 141. #421 | C2×C181 | semidirect |
| 142. #419 | C2×C181 | semidirect |
| 143. #410 | C2×C181 | semidirect |
| 144. #344 | C2×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #575×C181 | 2 |
| C2×#137×C181 | 2 |
| #536×C181 | 2 |
| #421×C181 | 2 |
| #419×C181 | 2 |
| #410×C181 | 2 |
| #344×C181 | 2 |
| #2009 | 181 |