Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
4638 conjugacy classes of subgroups; only the 1067 normal subgroups are shown.
This group has 4638 conjugacy classes of subgroups — too many to draw. Only its 1067 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D568 | C2 | semidirect |
| 2. C22×#14556125 | C2 | semidirect |
| 3. C2×#17986376 | C2 | direct (N × H) |
| 4. C22×C4×C8×C71 | C2 | semidirect |
| 8. C22×D568 | C22 | semidirect |
| 10. C2×#14556125 | C22 | semidirect |
| 11. #17986376 | C22 | direct (N × H) |
| 14. C2×C4×C8×C71 | C22 | semidirect |
| 22. C2×D568 | C23 | semidirect |
| 24. #14556125 | C23 | semidirect |
| 27. C22×C8×C71 | D4 | semidirect |
| 31. C4×C8×C71 | C23 | semidirect |
| 43. C22×C4×C71 | D8 | semidirect |
| 48. C2×C8×C71 | C2×D4 | semidirect |
| 60. C2×C4×C71 | C2×D8 | semidirect |
| 68. C8×C71 | C22×D4 | semidirect |
| 69. C22×C71 | #493 | semidirect |
| 77. C4×C71 | C22×D8 | semidirect |
| 80. C2×C71 | C2×#493 | semidirect |
| 87. C22×C4×C8 | D71 | semidirect |
| 88. C71 | C22×#493 | semidirect |
| 98. C2×C4×C8 | C2×D71 | semidirect |
| 109. C22×C8 | D284 | semidirect |
| 115. C4×C8 | C22×D71 | semidirect |
| 126. C22×C4 | D568 | semidirect |
| 132. C2×C8 | C2×D284 | semidirect |
| 147. C2×C4 | C2×D568 | semidirect |
| 152. C8 | C22×D284 | semidirect |
| 156. C22 | #17986376 | direct (N × H) |
| 161. C4 | C22×D568 | semidirect |
| 164. C2 | C2×#17986376 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D568 | 2 |
| C22×#14556125 | 2 |
| C2×#17986376 | 2 |
| C22×C4×C8×C71 | 2 |
| C22×#493 | 71 |