Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22627150 | C2 | semidirect |
| 2. #22627148 | C2 | semidirect |
| 3. #22626999 | C2 | semidirect |
| 4. #22626982 | C2 | semidirect |
| 5. #22626981 | C2 | semidirect |
| 6. #22626946 | C2 | semidirect |
| 42. #14556537 | C8 | semidirect |
| 43. #14556536 | C8 | semidirect |
| 44. #14556532 | C8 | semidirect |
| 46. SD32×C73 | C8 | semidirect |
| 110. C73 | #12047 | semidirect |
| 132. SD32 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627150 | 2 |
| #22627148 | 2 |
| #22626999 | 2 |
| #22626982 | 2 |
| #22626981 | 2 |
| #22626946 | 2 |
| #22626331 | 2 |
| #12047 | 73 |