Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
230 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 230 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 | C2×C4×C181 | C2×D4 |
| commutator | C2×C4 | C22×C4×C181 |
| Frattini, cosocle | C42 | C23×C181 |
| socle | C22×C181 | C2×C22⋊C4 |
| prime radical | #121×C181 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C181 ◁ C2×C42×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #432×C181 | C2 | semidirect |
| 3. C2×C4×C8×C181 | C2 | semidirect |
| 4. Q8⋊C8×C181 | C2 | semidirect |
| 5. D4⋊C8×C181 | C2 | semidirect |
| 90. C181 | #1494 | direct (N × H) |
| 91. #1494 | C181 | direct (N × H) |
| 93. #432 | C2×C181 | semidirect |
| 94. C2×C4×C8 | C2×C181 | semidirect |
| 95. Q8⋊C8 | C2×C181 | semidirect |
| 96. D4⋊C8 | C2×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #529×C181 | 2 |
| #432×C181 | 2 |
| C2×C4×C8×C181 | 2 |
| Q8⋊C8×C181 | 2 |
| D4⋊C8×C181 | 2 |
| #1494 | 181 |