Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
266 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 104 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 | C2×#41×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. #423×C181 | C2 | semidirect |
| 3. C4×M16×C181 | C2 | semidirect |
| 4. Q8⋊C8×C181 | C2 | semidirect |
| 5. D4⋊C8×C181 | C2 | semidirect |
| 55. Q8×C181 | M16 | semidirect |
| 58. D4×C181 | M16 | semidirect |
| 102. C181 | #1489 | direct (N × H) |
| 103. #1489 | C181 | direct (N × H) |
| 105. #423 | C2×C181 | semidirect |
| 106. C4×M16 | C2×C181 | semidirect |
| 107. Q8⋊C8 | C2×C181 | semidirect |
| 108. D4⋊C8 | C2×C181 | semidirect |
| 158. Q8 | M16×C181 | semidirect |
| 161. D4 | M16×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#41×C181 | 2 |
| #423×C181 | 2 |
| C4×M16×C181 | 2 |
| Q8⋊C8×C181 | 2 |
| D4⋊C8×C181 | 2 |
| #1489 | 181 |