Finite Group DatabasebetaFinite Group DatabasebetaOrder 17672.
18 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic2209 | C2 | 1 | 2 | yes | maximal |
| 2 | C4×C2209 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×C2209 | C22 | 1 | 1 | yes | characteristic |
| 4 | C2209 | Q8 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 5 | Dic94 | — | 47 | 1 | no | maximal |
| 6 | C4×C47 | D47 | 1 | 1 | yes | characteristic |
| 7 | Dic47 | — | 47 | 2 | no | — |
| 8 | C2×C47 | C2×D47 | 1 | 1 | yes | characteristic |
| 9 | C47 | Dic94 | 1 | 1 | yes | characteristic |
| 10 | Q8 | — | 2209 | 1 | no | Sylow |
| 11 | C4 | — | 2209 | 2 | no | — |
| 12 | C4 | D2209 | 1 | 1 | yes | characteristic |
| 13 | C2 | C2×D2209 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D2209 |
| commutator, cosocle | C2×C2209 | C22 |
| Frattini, socle, prime radical | C2×C47 | C2×D47 |
| Fitting | C4×C2209 | C2 |
| hypercenter | C4 | D2209 |
| hypocenter | C2209 | Q8 |
| LCS | G ▷ C2×C2209 ▷ C2209 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2209 | Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic2209 | 2 |
| C4×C2209 | 2 |
| Dic94 | 47 |