Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1382 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 382 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×C67 | #99 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C2×Q8 | C24×C67 |
| prime radical | C23×D4×C67 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C24×C67 ◁ C23×Q8×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#101×C67 | C2 | semidirect |
| 3. C2×#355×C67 | C2 | direct (N × H) |
| 13. C2×#101×C67 | C22 | semidirect |
| 14. #355×C67 | C22 | direct (N × H) |
| 40. #101×C67 | C23 | semidirect |
| 116. C22×C67 | #355 | direct (N × H) |
| 125. C22×#355 | C67 | direct (N × H) |
| 129. C2×C67 | C2×#355 | direct (N × H) |
| 132. C22×#101 | C2×C67 | semidirect |
| 133. C2×#355 | C2×C67 | direct (N × H) |
| 134. C67 | C22×#355 | direct (N × H) |
| 144. C2×#101 | C22×C67 | semidirect |
| 145. #355 | C22×C67 | direct (N × H) |
| 171. #101 | C23×C67 | semidirect |
| 247. C22 | #355×C67 | direct (N × H) |
| 259. C2 | C2×#355×C67 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#124×C67 | 2 |
| C22×#101×C67 | 2 |
| C2×#355×C67 | 2 |
| C22×#355 | 67 |