Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
240 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | #99 |
| commutator | C2×C4 | C22×C4×C151 |
| Frattini, cosocle | C2×Q8 | C23×C151 |
| prime radical | C23×C151 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C23×C151 ◁ C22×Q8×C151 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #356×C151 | C2 | direct (N × H) |
| 66. C2×C151 | #356 | direct (N × H) |
| 68. C151 | C2×#356 | direct (N × H) |
| 69. C2×#356 | C151 | direct (N × H) |
| 72. #356 | C2×C151 | direct (N × H) |
| 135. C2 | #356×C151 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Q8×C151 | 2 |
| C2×#101×C151 | 2 |
| #356×C151 | 2 |
| C2×#356 | 151 |