Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
912 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22599278 | C2 | semidirect |
| 3. #22587009 | C2 | semidirect |
| 4. #22586173 | C2 | semidirect |
| 5. C71×#1994 | C2 | semidirect |
| 31. C4⋊(C71⋊C8) | D4 | semidirect |
| 36. C4⋊Q8×C71 | D4 | semidirect |
| 73. C42×C71 | SD16 | semidirect |
| 124. #1994 | D71 | semidirect |
| 127. C71 | #10290 | semidirect |
| 147. C4⋊Q8 | D284 | semidirect |
| 195. C42 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599278 | 2 |
| #22596735 | 2 |
| #22587009 | 2 |
| #22586173 | 2 |
| C71×#1994 | 2 |
| #10290 | 71 |