Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1342 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 283 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. C2×#17986376 | C2 | semidirect |
| 2. C2×#17986375 | C2 | semidirect |
| 3. #22587954 | C2 | direct (N × H) |
| 4. C2×C8×C71⋊C8 | C2 | semidirect |
| 5. C2×#493×C71 | C2 | semidirect |
| 10. #17986376 | C22 | semidirect |
| 12. #17986375 | C22 | semidirect |
| 14. C8×C71⋊C8 | C22 | semidirect |
| 18. #493×C71 | C22 | semidirect |
| 52. C2×C71⋊C8 | D8 | semidirect |
| 64. C2×C8×C71 | D8 | semidirect |
| 90. C8×C71 | C2×D8 | semidirect |
| 91. C71⋊C8 | C2×D8 | semidirect |
| 107. C2×C71 | #1712 | semidirect |
| 113. C2×#493 | D71 | semidirect |
| 116. C71 | C2×#1712 | semidirect |
| 127. #493 | C2×D71 | semidirect |
| 175. C2×C8 | #11765850 | semidirect |
| 202. C8 | C2×#11765850 | semidirect |
| 218. C2 | #22587954 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986376 | 2 |
| C2×#17986375 | 2 |
| #22587954 | 2 |
| C2×C8×C71⋊C8 | 2 |
| C2×#493×C71 | 2 |
| C2×#1712 | 71 |