Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
334 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C181 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C181 |
| Frattini, cosocle | C22×C4 | C23×C181 |
| prime radical | #525×C181 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C181 ◁ C23×C4×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #407×C181 | C2 | semidirect |
| 3. C2×#95×C181 | C2 | semidirect |
| 4. #328×C181 | C2 | semidirect |
| 5. #327×C181 | C2 | semidirect |
| 6. C2×#41×C181 | C4 | semidirect |
| 11. C22⋊Q8×C181 | C4 | semidirect |
| 13. #121×C181 | C4 | semidirect |
| 18. #117×C181 | C4 | semidirect |
| 25. C2×Q8×C181 | C2×C4 | semidirect |
| 29. C2×D4×C181 | C2×C4 | semidirect |
| 46. C4⋊C4×C181 | C2×C4 | semidirect |
| 47. C4⋊C4×C181 | C2×C4 | semidirect |
| 119. C181 | #1504 | direct (N × H) |
| 120. #1504 | C181 | direct (N × H) |
| 122. #407 | C2×C181 | semidirect |
| 123. C2×#95 | C2×C181 | semidirect |
| 124. #328 | C2×C181 | semidirect |
| 125. #327 | C2×C181 | semidirect |
| 126. C2×#41 | C4×C181 | semidirect |
| 131. C22⋊Q8 | C4×C181 | semidirect |
| 133. #121 | C4×C181 | semidirect |
| 138. #117 | C4×C181 | semidirect |
| 145. C2×Q8 | C2×C4×C181 | semidirect |
| 149. C2×D4 | C2×C4×C181 | semidirect |
| 166. C4⋊C4 | C2×C4×C181 | semidirect |
| 167. C4⋊C4 | C2×C4×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #525×C181 | 2 |
| #407×C181 | 2 |
| C2×#95×C181 | 2 |
| #328×C181 | 2 |
| #327×C181 | 2 |
| #1504 | 181 |