Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
912 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22599281 | C2 | semidirect |
| 2. #22589317 | C2 | semidirect |
| 3. #22587008 | C2 | semidirect |
| 4. #22586173 | C2 | semidirect |
| 21. #14556128 | D4 | semidirect |
| 27. C4⋊(C71⋊C8) | D4 | semidirect |
| 73. C42×C71 | SD16 | semidirect |
| 127. C71 | #10290 | semidirect |
| 195. C42 | #11765853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599281 | 2 |
| #22589317 | 2 |
| #22587008 | 2 |
| #22586173 | 2 |
| C71×#2867 | 2 |
| #10290 | 71 |