Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
480 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 208 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C181 |
| prime radical | C2×#41×C181 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C181 ◁ C2×C42×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4⋊Q8×C181 | C2 | semidirect |
| 4. #462×C181 | C2 | semidirect |
| 5. #461×C181 | C2 | semidirect |
| 6. #423×C181 | C2 | semidirect |
| 7. #419×C181 | C2 | semidirect |
| 90. C4×C181 | #137 | semidirect |
| 97. C181 | #3039 | direct (N × H) |
| 98. #3039 | C181 | direct (N × H) |
| 100. C2×C4⋊Q8 | C2×C181 | semidirect |
| 102. #462 | C2×C181 | semidirect |
| 103. #461 | C2×C181 | semidirect |
| 104. #423 | C2×C181 | semidirect |
| 105. #419 | C2×C181 | semidirect |
| 188. C4 | #137×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 |
| C2×C4⋊Q8×C181 | 2 |
| C4×#41×C181 | 2 |
| #462×C181 | 2 |
| #461×C181 | 2 |
| #423×C181 | 2 |
| #419×C181 | 2 |
| #3039 | 181 |