Finite Group DatabasebetaFinite Group DatabasebetaOrder 18734.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C17×C19×C29 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D551 | — | 17 | 1 | no | maximal, Hall |
| 3 | D493 | — | 19 | 1 | no | maximal, Hall |
| 4 | D323 | — | 29 | 1 | no | maximal, Hall |
| 5 | C19×C29 | D17 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | C17×C29 | D19 | 1 | 1 | yes | characteristic, complemented, Hall |
| 7 | C17×C19 | D29 | 1 | 1 | yes | characteristic, complemented, Hall |
| 8 | D29 | — | 323 | 1 | no | Hall |
| 9 | D19 | — | 493 | 1 | no | Hall |
| 10 | D17 | — | 551 | 1 | no | Hall |
| 11 | C29 | D323 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C19 | D493 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 13 | C17 | D551 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2 | — | 9367 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C19×C29 | C2 |
| LCS | G ▷ C17×C19×C29 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×C19×C29 | C2 | semidirect |
| 5. C19×C29 | D17 | semidirect |
| 6. C17×C29 | D19 | semidirect |
| 7. C17×C19 | D29 | semidirect |
| 11. C29 | D323 | semidirect |
| 12. C19 | D493 | semidirect |
| 13. C17 | D551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×C19×C29 | 2 |
| D551 | 17 |
| D493 | 19 |
| D323 | 29 |