Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
950 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 950 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. #22599260 | C2 | semidirect |
| 2. #22596735 | C2 | semidirect |
| 3. #22589168 | C2 | semidirect |
| 4. #22587007 | C2 | semidirect |
| 5. C71×#1276 | C2 | semidirect |
| 26. #14556128 | D4 | semidirect |
| 34. #14556125 | D4 | semidirect |
| 44. C4⋊C8×C71 | D4 | semidirect |
| 78. C42×C71 | D8 | semidirect |
| 140. #1276 | D71 | semidirect |
| 141. C71 | #10280 | semidirect |
| 178. C4⋊C8 | D284 | semidirect |
| 214. C42 | D568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599260 | 2 |
| #22596735 | 2 |
| #22589168 | 2 |
| #22587007 | 2 |
| C71×#1276 | 2 |
| #10280 | 71 |