Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
794 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22597806 | C2 | semidirect |
| 3. #22593282 | C2 | semidirect |
| 4. #22587009 | C2 | semidirect |
| 5. #22586834 | C2 | semidirect |
| 6. #22586730 | C2 | semidirect |
| 7. C71×#1303 | C2 | semidirect |
| 43. #14556128 | D4 | semidirect |
| 50. #14556125 | D4 | semidirect |
| 75. C4⋊C8×C71 | D4 | semidirect |
| 76. C4⋊C8×C71 | D4 | semidirect |
| 110. C2×D284 | D8 | semidirect |
| 247. #1303 | D71 | semidirect |
| 248. C71 | #10238 | semidirect |
| 311. C4⋊C8 | D284 | semidirect |
| 312. C4⋊C8 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599260 | 2 |
| #22597806 | 2 |
| #22593282 | 2 |
| #22587009 | 2 |
| #22586834 | 2 |
| #22586730 | 2 |
| C71×#1303 | 2 |
| #10238 | 71 |