Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
394 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 92 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 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C181 |
| prime radical | #535×C181 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C181 ◁ C22×C4×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#137×C181 | C2 | semidirect |
| 3. C2×#124×C181 | C2 | semidirect |
| 4. C2×#104×C181 | C2 | semidirect |
| 5. #419×C181 | C2 | semidirect |
| 6. C2×#100×C181 | C2 | semidirect |
| 7. #339×C181 | C2 | semidirect |
| 40. C2×Q8×C181 | D4 | semidirect |
| 59. M16×C181 | D4 | semidirect |
| 68. C42×C181 | D4 | semidirect |
| 131. C181 | #2004 | direct (N × H) |
| 132. #2004 | C181 | direct (N × H) |
| 133. C2×#137 | C2×C181 | semidirect |
| 135. C2×#124 | C2×C181 | semidirect |
| 136. C2×#104 | C2×C181 | semidirect |
| 137. #419 | C2×C181 | semidirect |
| 138. C2×#100 | C2×C181 | semidirect |
| 139. #339 | C2×C181 | semidirect |
| 172. C2×Q8 | D4×C181 | semidirect |
| 191. M16 | D4×C181 | semidirect |
| 200. C42 | D4×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#137×C181 | 2 |
| #535×C181 | 2 |
| C2×#124×C181 | 2 |
| C2×#104×C181 | 2 |
| #419×C181 | 2 |
| C2×#100×C181 | 2 |
| #339×C181 | 2 |
| #2004 | 181 |