Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
602 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 155 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. #22620511 | C2 | semidirect |
| 2. #22612181 | C2 | semidirect |
| 3. #22612156 | C2 | semidirect |
| 4. #22612018 | C2 | semidirect |
| 5. #22611777 | C2 | semidirect |
| 6. C4×C16×D73 | C2 | semidirect |
| 7. C73×#2252 | C2 | semidirect |
| 76. C16×C73 | #41 | semidirect |
| 96. C4×D73 | D16 | semidirect |
| 123. #2252 | D73 | semidirect |
| 129. C73 | #33733 | semidirect |
| 198. C16 | #11924029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620511 | 2 |
| #22612181 | 2 |
| #22612156 | 2 |
| #22612018 | 2 |
| #22611777 | 2 |
| C4×C16×D73 | 2 |
| C73×#2252 | 2 |
| #33733 | 73 |