Finite Group DatabasebetaFinite Group DatabasebetaOrder 24.
11 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | A4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D4 | — | 3 | 1 | no | maximal, Sylow |
| 3 | D3 | — | 4 | 1 | no | maximal |
| 4 | C22 | — | 3 | 1 | no | — |
| 5 | C22 | D3 | 1 | 1 | yes | characteristic, complemented |
| 6 | C4 | — | 3 | 1 | no | — |
| 7 | C3 | — | 4 | 1 | no | Sylow |
| 8 | C2 | — | 3 | 1 | no | — |
| 9 | C2 | — | 6 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A4 | C2 |
| Fitting, socle | C22 | D3 |
| LCS | G ▷ A4 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. A4 | C2 | semidirect |
| 5. C22 | D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4 | 2 |
| D4 | 3 |
| D3 | 4 |