Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
316 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C149 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C149 |
| prime radical | C24×C149 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C149 ◁ C23×C4×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#107×C149 | C2 | semidirect |
| 3. C2×#103×C149 | C2 | semidirect |
| 4. C2×#103×C149 | C2 | semidirect |
| 7. #340×C149 | C2 | semidirect |
| 129. C149 | #2036 | direct (N × H) |
| 130. #2036 | C149 | direct (N × H) |
| 132. C2×#107 | C2×C149 | semidirect |
| 133. C2×#103 | C2×C149 | semidirect |
| 134. C2×#103 | C2×C149 | semidirect |
| 137. #340 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊Q8×C149 | 2 |
| C2×#107×C149 | 2 |
| C2×#103×C149 | 2 |
| C2×C22⋊C8×C149 | 2 |
| #380×C149 | 2 |
| #340×C149 | 2 |
| #2036 | 149 |