Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
912 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22599283 | C2 | semidirect |
| 2. #22599281 | C2 | semidirect |
| 4. #22589316 | C2 | semidirect |
| 5. #22587009 | C2 | semidirect |
| 6. #22586172 | C2 | semidirect |
| 7. C71×#1545 | C2 | semidirect |
| 35. #14556128 | D4 | semidirect |
| 36. #14556128 | D4 | semidirect |
| 54. C4⋊(C71⋊C8) | D4 | semidirect |
| 70. C4⋊C8×C71 | D4 | semidirect |
| 104. C4×Dic71 | SD16 | semidirect |
| 204. #1545 | D71 | semidirect |
| 206. C71 | #10290 | semidirect |
| 265. C4⋊C8 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599283 | 2 |
| #22599281 | 2 |
| #22596734 | 2 |
| #22589316 | 2 |
| #22587009 | 2 |
| #22586172 | 2 |
| C71×#1545 | 2 |
| #10290 | 71 |