Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
236 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 72 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 | C42 | C23×C181 |
| prime radical | #459×C181 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C181 ◁ C42×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #554×C181 | C2 | semidirect |
| 2. #492×C181 | C2 | semidirect |
| 3. #460×C181 | C2 | semidirect |
| 5. #333×C181 | C2 | semidirect |
| 6. Q8⋊C8×C181 | C2 | semidirect |
| 7. D4⋊C8×C181 | C2 | semidirect |
| 61. D4×C181 | SD16 | semidirect |
| 96. C181 | #1622 | direct (N × H) |
| 97. #1622 | C181 | direct (N × H) |
| 98. #554 | C2×C181 | semidirect |
| 99. #492 | C2×C181 | semidirect |
| 100. #460 | C2×C181 | semidirect |
| 102. #333 | C2×C181 | semidirect |
| 103. Q8⋊C8 | C2×C181 | semidirect |
| 104. D4⋊C8 | C2×C181 | semidirect |
| 158. D4 | SD16×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #554×C181 | 2 |
| #492×C181 | 2 |
| #460×C181 | 2 |
| #459×C181 | 2 |
| #333×C181 | 2 |
| Q8⋊C8×C181 | 2 |
| D4⋊C8×C181 | 2 |
| #1622 | 181 |