Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
176 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 100 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 | C4 | C22×C8×C181 |
| Frattini, cosocle | C42 | C23×C181 |
| socle | C22×C181 | C4×D4 |
| prime radical | C2×D4×C181 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C181 ◁ C4×C8×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C8×Q8×C181 | C2 | semidirect |
| 4. #335×C181 | C2 | semidirect |
| 5. Q8⋊C8×C181 | C2 | semidirect |
| 7. #322×C181 | C2 | semidirect |
| 26. SD16×C181 | C8 | semidirect |
| 43. Q8×C181 | C2×C8 | semidirect |
| 60. C8×C181 | C2×C8 | semidirect |
| 77. C181 | SD16⋊C8 | direct (N × H) |
| 78. SD16⋊C8 | C181 | direct (N × H) |
| 79. C8×Q8 | C2×C181 | semidirect |
| 82. #335 | C2×C181 | semidirect |
| 83. Q8⋊C8 | C2×C181 | semidirect |
| 85. #322 | C2×C181 | semidirect |
| 104. SD16 | C8×C181 | semidirect |
| 121. Q8 | C2×C8×C181 | semidirect |
| 138. C8 | C2×C8×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Q8×C181 | 2 |
| C4×SD16×C181 | 2 |
| C8×D4×C181 | 2 |
| #335×C181 | 2 |
| Q8⋊C8×C181 | 2 |
| D4⋊C8×C181 | 2 |
| #322×C181 | 2 |
| SD16⋊C8 | 181 |